https://www.predictivestatmech.org/w/api.php?action=feedcontributions&user=David+M.+Rogers&feedformat=atomPredictive Chemistry - User contributions [en]2022-10-02T03:33:22ZUser contributionsMediaWiki 1.27.4https://www.predictivestatmech.org/w/index.php?title=Main_Page&diff=757Main Page2020-01-17T15:11:03Z<p>David M. Rogers: </p>
<hr />
<div>Predictivestatmech.org shows off predictive models for new physics and chemistry that appear<br />
when moving up from the atomic to the nano and micro-scale. To support this<br />
goal, we are developing the thermodynamics of far-from equilibrium systems,<br />
building functional data structures for supercomputing and applying Bayesian<br />
inference to mine simulation data. Work in these topics builds on recent<br />
advances in fundamental computer science, applied statistics, and<br />
nonequilibrium physics and chemistry. Together, new developments in these<br />
fields will allow unprecedented access to electron through device-level<br />
simulations and analysis for materials design grounded in fundamental physics.<br />
<br />
Two research areas collectively have the potential to<br />
greatly reduce the time and effort building, running, and analyzing<br />
molecular and continuum simulations for modern high-performance<br />
computing platforms.<br />
The first expands the theory and techniques of statistical<br />
mechanics for probabilistic simulation of energy conversion<br />
devices. The second applies advances in domain-specific languages<br />
to eliminate the lag between defining a physical, Hamiltonian model and carrying<br />
out dynamics and other computations on its potential energy<br />
landscape.<br />
<br />
For more details, see the [[Research]], [[Publications]], and [[Predictive_Chemistry:Current_events|Current events]] links.</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=PChemFall2019&diff=756PChemFall20192019-10-31T21:10:01Z<p>David M. Rogers: /* Topics */</p>
<hr />
<div>'''<BIG>Physical Chemistry I</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4410-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Aug. 27 - Nov. 26, 2019<br />
* Meeting Times: Tues. and Thurs., 3:30-4:45 pm in CIS 3064<br />
** Regular quizzes on Tuesdays<br />
** Problem Sessions: Fri., 2-2:50 pm in CIS 3064<br />
** Office Hours: by request and TBA<br />
<br />
* Grading:<br />
** Quiz (25%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (25%) Thurs., Sept. 26 3:30-4:45 pm (CIS 3064)<br />
** Exam 2 (25%) Thurs., Oct. 24 3:30-4:45 pm (CIS 3064)<br />
** [[#Final Project]] (25%) due Tues., Nov. 26 3:30 pm (Canvas or CIS 3064)<br />
<br />
== Overview ==<br />
<br />
This is the first part of a 2-semester course in thermodynamics. This course will cover the mathematical theory of chemical equilibrium, heat, and work. These are the driving forces behind the operation of Le Châtelier's principle, and are routinely used to understand and control chemical reactions, states of matter, and amount and efficiency of energy production.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
<br />
== Resources ==<br />
<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/ktcon.html Kinetic Theory] at HyperPhysics<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html Heat Concepts] at HyperPhysics<br />
** Note: McQuarrie says dU = dQ + dW, while Nave says dU = dQ - dW. There is no contradiction, since McQuarrie's dW = -P dV (work done on the system), while Nave's dW = P dV (work done by the system). I prefer the first definition.<br />
* News from the frontlines of exploring entropy: [http://scitation.aip.org/content/aip/magazine/physicstoday/article/68/9/10.1063/PT.3.2912 Information: From Maxwell’s demon to Landauer’s eraser]<br />
* [[Media:Transforms.pdf|Notes]] on transformations of variables.<br />
* [[PChemFall2018 | Course Page from 2018]]<br />
* [[PChemFall2017 | Course Page from 2017]]<br />
* [[PChemFall2016 | Course Page from 2016]]<br />
* [[PChemFall2015 | Course Page from 2015]] -- contains previous quizzes and keys.<br />
* [https://predictivestatmech.org/papers/quiz0.pdf Pretest key]<br />
* [https://predictivestatmech.org/papers/quiz1_2018.pdf Quiz 1 Key] -- for more information and practice problems, see The Vallance Chemistry Group, U. Oxford (http://vallance.chem.ox.ac.uk under Teaching -> Units and Dimensions).<br />
* Gas Thermodynamics Videos:<br />
** P-V work demonstrated by a [https://youtu.be/j0TQxYemrgg?t=75 Steel Drum Implosion]<br />
** Adiabatic Compression in a [https://youtu.be/4qe1Ueifekg?t=144 Fire Piston]<br />
** Complete thermodynamic cycle [https://youtu.be/EtF3-YmHp_0?t=29 Stirling Engine]<br />
** Pressure (concentration gradient) driven chemical work [https://youtu.be/3y1dO4nNaKY?t=95 ATP Synthetase]<br />
<br />
== Topics ==<br />
<br />
# Moving Freely in P-V-T space (Chapter H, with examples from Ch. 16-[2,3,5,6,7], 17-[4,5], and 19-1)<br />
#* Isobaric, isothermal, and isochoric processes<br />
#* State functions<br />
#* Implicit, partial, and total derivatives<br />
#* Integration along a path<br />
#* Relations between partial derivatives<br />
#** Transformations using substitution<br />
#** Transformations using the chain rule<br />
#* Visualizing isosurfaces<br />
#* Using P(V,T) / V(P,T) / T(P,V)<br />
# First Law of Thermodynamics – conserved quantities (Ch. 19-[2 to 9])<br />
#* Mechanisms of energy flow: work, heat, mass/chemical<br />
#* Integrating work and heat for common processes<br />
#* Energy of a molecule vs. a collection – translation, rotation, intermolecular, etc.<br />
#* Extensive and intensive quantities<br />
#* Using energy balance for fun and profit.<br />
# Standard States and Energies (Ch. 19-[10,11,12], Ch 26-[3,6,7,8,9])<br />
#* Connecting to analytical chemistry.<br />
#* Spontaneous, irreversible, processes vs. quasistatic processes.<br />
#* Experimentally measuring reaction constants and heats. (Ch. 21-5)<br />
# The Second Law of Thermodynamics: Energy, Enthalpy, Entropy, and Free Energy (Ch. 20)<br />
#* The absolute temperature scale. (Ch. 16-1)<br />
#* Inequalities followed by each path type. (Ch. 22-[1,2])<br />
#* Heat, measurement, information, Maxwell’s demon and Landauer’s principle.<br />
# Basic Probability<br />
#* Simple counting (Ch. J)<br />
#* Velocity distribution function (Ch 27-[1,2,3,4])<br />
#* Boltzmann distributions (Ch. 17-[1,2,3,6 to 8])<br />
# Applications:<br />
#* Quantitative Prediction of Reaction Equilibria (Ch. 26)<br />
#* Liquid solutions: osmotic pressure, vapor pressure, Henry’s and Raoult’s Laws (Ch. 24)<br />
#* Phase Equilibria and Basic Phase Diagrams (Ch. 23)<br />
#* Thermodynamic Cycles, Examples with Refrigeration and Galvanic Cell (Ch. 20-7)<br />
#* [https://{{SERVERNAME}}/papers/chempot.pdf Standard expressions for the chemical potential]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Moving Freely in P-V-T space<br />
#* H: 1-5,7,10-14<br />
#* 16:1-21,25,26(1st part),29,35-42,44-45,52-56,58-59,33(optional)<br />
#** sketch a plot for 16.4 and 16.5<br />
#* 17: 9-17<br />
# First Law (sec. 19-1 through 19-9)<br />
#* 19:1-31<br />
#* You can skip 19-27 and 28 (we'll do in class)<br />
# Standard States and Energies (sec. 19-10 through 19-12, 21-5 and 26-3 through 26-9)<br />
#* 19:34-49<br />
#* 21: 1-7, 10-26, 29, 48, 42-43, 45-47<br />
#* 26: 2,6,8-11,13,16-17,21<br />
#* 26: 61 -- only integrate dG = V dP at constant V=1/rho.<br />
# Entropy, Free Energy and the Second Law (all of Ch. 20, sections 16:1, 22:1-2)<br />
#* 20: 2-4, 6-16, 18-19, 24-25, 27-30, 32-33<br />
#* 22: 1-5 (for 4 and 5 use 1st law and Gibbs relation from A)<br />
#* 16: 4,6-11<br />
# Basic Probability (Ch. J, 17 and 27)<br />
#* J: 1-7<br />
#* 17: 1, 3, 4, 7-8 [for 7, use a 3-state system with E(0) = 0, E(-1) = -1, E(1) = 1]<br />
#* 27:1-9<br />
# Applications:<br />
## Reaction Equilibria (Ch. 26)<br />
##* 26: 3-7, 12, 14-15, 33, 59, 61, 62-65<br />
## Phase Equilibria and Basic Phase Diagrams (Ch. 23)<br />
## Liquid Solutions: Osmotic Pressure, Henry's and Raoult's Law (Ch. 24)<br />
<br />
== Final Project ==<br />
<br />
[https://{{SERVERNAME}}/papers/final_project.pdf A description of the final project is here].<br />
<br />
== Online Tutorials ==<br />
<br />
There are some excellent introductory videos on Khan Academy that are useful if you need a refresher or extra practice with some of the topics in the course.<br />
<br />
# Moving Freely in P-V-T space<br />
#* Isobars & Work [https://www.khanacademy.org/test-prep/mcat/chemical-processes/thermodynamics-mcat/v/pv-diagrams-part-1-work-and-isobaric-processes]<br />
#* Isotherms, Isochors, Adiabats [https://www.khanacademy.org/test-prep/mcat/chemical-processes/thermodynamics-mcat/v/pv-diagrams-part-2-isothermal-isometric-adiabatic-processes]<br />
#* Implicit Derivatives (explained with practice problems) [https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-implicit-diff/v/implicit-differentiation-1]<br />
#* Partial Derivatives (explained with practice problems) [https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivatives/v/partial-derivatives-introduction]<br />
#* State Functions (Macrostates vs Microstates) [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/macrostates-and-microstates]<br />
#* Quasistatic and Reversible Processes [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/quasistatic-and-reversible-processes]<br />
#* Integration along a path (using PV-diagrams and expansion/compression Work) [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/pv-diagrams-and-expansion-work]<br />
# First Law of Thermodynamics – conserved quantities (Ch. 19-[2 to 9])<br />
#* PV work [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/a/pressure-volume-work]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=PChemFall2019&diff=755PChemFall20192019-10-17T18:33:48Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry I</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4410-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Aug. 27 - Nov. 26, 2019<br />
* Meeting Times: Tues. and Thurs., 3:30-4:45 pm in CIS 3064<br />
** Regular quizzes on Tuesdays<br />
** Problem Sessions: Fri., 2-2:50 pm in CIS 3064<br />
** Office Hours: by request and TBA<br />
<br />
* Grading:<br />
** Quiz (25%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (25%) Thurs., Sept. 26 3:30-4:45 pm (CIS 3064)<br />
** Exam 2 (25%) Thurs., Oct. 24 3:30-4:45 pm (CIS 3064)<br />
** [[#Final Project]] (25%) due Tues., Nov. 26 3:30 pm (Canvas or CIS 3064)<br />
<br />
== Overview ==<br />
<br />
This is the first part of a 2-semester course in thermodynamics. This course will cover the mathematical theory of chemical equilibrium, heat, and work. These are the driving forces behind the operation of Le Châtelier's principle, and are routinely used to understand and control chemical reactions, states of matter, and amount and efficiency of energy production.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
<br />
== Resources ==<br />
<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/ktcon.html Kinetic Theory] at HyperPhysics<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html Heat Concepts] at HyperPhysics<br />
** Note: McQuarrie says dU = dQ + dW, while Nave says dU = dQ - dW. There is no contradiction, since McQuarrie's dW = -P dV (work done on the system), while Nave's dW = P dV (work done by the system). I prefer the first definition.<br />
* News from the frontlines of exploring entropy: [http://scitation.aip.org/content/aip/magazine/physicstoday/article/68/9/10.1063/PT.3.2912 Information: From Maxwell’s demon to Landauer’s eraser]<br />
* [[Media:Transforms.pdf|Notes]] on transformations of variables.<br />
* [[PChemFall2018 | Course Page from 2018]]<br />
* [[PChemFall2017 | Course Page from 2017]]<br />
* [[PChemFall2016 | Course Page from 2016]]<br />
* [[PChemFall2015 | Course Page from 2015]] -- contains previous quizzes and keys.<br />
* [https://predictivestatmech.org/papers/quiz0.pdf Pretest key]<br />
* [https://predictivestatmech.org/papers/quiz1_2018.pdf Quiz 1 Key] -- for more information and practice problems, see The Vallance Chemistry Group, U. Oxford (http://vallance.chem.ox.ac.uk under Teaching -> Units and Dimensions).<br />
* Gas Thermodynamics Videos:<br />
** P-V work demonstrated by a [https://youtu.be/j0TQxYemrgg?t=75 Steel Drum Implosion]<br />
** Adiabatic Compression in a [https://youtu.be/4qe1Ueifekg?t=144 Fire Piston]<br />
** Complete thermodynamic cycle [https://youtu.be/EtF3-YmHp_0?t=29 Stirling Engine]<br />
** Pressure (concentration gradient) driven chemical work [https://youtu.be/3y1dO4nNaKY?t=95 ATP Synthetase]<br />
<br />
== Topics ==<br />
<br />
# Moving Freely in P-V-T space (Chapter H, with examples from Ch. 16-[2,3,5,6,7], 17-[4,5], and 19-1)<br />
#* Isobaric, isothermal, and isochoric processes<br />
#* State functions<br />
#* Implicit, partial, and total derivatives<br />
#* Integration along a path<br />
#* Relations between partial derivatives<br />
#** Transformations using substitution<br />
#** Transformations using the chain rule<br />
#* Visualizing isosurfaces<br />
#* Using P(V,T) / V(P,T) / T(P,V)<br />
# First Law of Thermodynamics – conserved quantities (Ch. 19-[2 to 9])<br />
#* Mechanisms of energy flow: work, heat, mass/chemical<br />
#* Integrating work and heat for common processes<br />
#* Energy of a molecule vs. a collection – translation, rotation, intermolecular, etc.<br />
#* Extensive and intensive quantities<br />
#* Using energy balance for fun and profit.<br />
# Standard States and Energies (Ch. 19-[10,11,12], Ch 26-[3,6,7,8,9])<br />
#* Connecting to analytical chemistry.<br />
#* Spontaneous, irreversible, processes vs. quasistatic processes.<br />
#* Experimentally measuring reaction constants and heats. (Ch. 21-5)<br />
# The Second Law of Thermodynamics: Energy, Enthalpy, Entropy, and Free Energy (Ch. 20)<br />
#* The absolute temperature scale. (Ch. 16-1)<br />
#* Inequalities followed by each path type. (Ch. 22-[1,2])<br />
#* Heat, measurement, information, Maxwell’s demon and Landauer’s principle.<br />
# Basic Probability<br />
#* Simple counting (Ch. J)<br />
#* Velocity distribution function (Ch 27-[1,2,3,4])<br />
#* Boltzmann distributions (Ch. 17-[1,2,3,6 to 8])<br />
# Applications:<br />
#* Quantitative Prediction of Reaction Equilibria (Ch. 26)<br />
#* Liquid solutions: osmotic pressure, vapor pressure, Henry’s and Raoult’s Laws (Ch. 24)<br />
#* Phase Equilibria and Basic Phase Diagrams (Ch. 23)<br />
#* Thermodynamic Cycles, Examples with Refrigeration and Galvanic Cell (Ch. 20-7)<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Moving Freely in P-V-T space<br />
#* H: 1-5,7,10-14<br />
#* 16:1-21,25,26(1st part),29,35-42,44-45,52-56,58-59,33(optional)<br />
#** sketch a plot for 16.4 and 16.5<br />
#* 17: 9-17<br />
# First Law (sec. 19-1 through 19-9)<br />
#* 19:1-31<br />
#* You can skip 19-27 and 28 (we'll do in class)<br />
# Standard States and Energies (sec. 19-10 through 19-12, 21-5 and 26-3 through 26-9)<br />
#* 19:34-49<br />
#* 21: 1-7, 10-26, 29, 48, 42-43, 45-47<br />
#* 26: 2,6,8-11,13,16-17,21<br />
#* 26: 61 -- only integrate dG = V dP at constant V=1/rho.<br />
# Entropy, Free Energy and the Second Law (all of Ch. 20, sections 16:1, 22:1-2)<br />
#* 20: 2-4, 6-16, 18-19, 24-25, 27-30, 32-33<br />
#* 22: 1-5 (for 4 and 5 use 1st law and Gibbs relation from A)<br />
#* 16: 4,6-11<br />
# Basic Probability (Ch. J, 17 and 27)<br />
#* J: 1-7<br />
#* 17: 1, 3, 4, 7-8 [for 7, use a 3-state system with E(0) = 0, E(-1) = -1, E(1) = 1]<br />
#* 27:1-9<br />
# Applications:<br />
## Reaction Equilibria (Ch. 26)<br />
##* 26: 3-7, 12, 14-15, 33, 59, 61, 62-65<br />
## Phase Equilibria and Basic Phase Diagrams (Ch. 23)<br />
## Liquid Solutions: Osmotic Pressure, Henry's and Raoult's Law (Ch. 24)<br />
<br />
== Final Project ==<br />
<br />
[https://{{SERVERNAME}}/papers/final_project.pdf A description of the final project is here].<br />
<br />
== Online Tutorials ==<br />
<br />
There are some excellent introductory videos on Khan Academy that are useful if you need a refresher or extra practice with some of the topics in the course.<br />
<br />
# Moving Freely in P-V-T space<br />
#* Isobars & Work [https://www.khanacademy.org/test-prep/mcat/chemical-processes/thermodynamics-mcat/v/pv-diagrams-part-1-work-and-isobaric-processes]<br />
#* Isotherms, Isochors, Adiabats [https://www.khanacademy.org/test-prep/mcat/chemical-processes/thermodynamics-mcat/v/pv-diagrams-part-2-isothermal-isometric-adiabatic-processes]<br />
#* Implicit Derivatives (explained with practice problems) [https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-implicit-diff/v/implicit-differentiation-1]<br />
#* Partial Derivatives (explained with practice problems) [https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivatives/v/partial-derivatives-introduction]<br />
#* State Functions (Macrostates vs Microstates) [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/macrostates-and-microstates]<br />
#* Quasistatic and Reversible Processes [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/quasistatic-and-reversible-processes]<br />
#* Integration along a path (using PV-diagrams and expansion/compression Work) [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/pv-diagrams-and-expansion-work]<br />
# First Law of Thermodynamics – conserved quantities (Ch. 19-[2 to 9])<br />
#* PV work [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/a/pressure-volume-work]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses&diff=754Courses2019-09-10T17:55:46Z<p>David M. Rogers: add Fall 2019 link</p>
<hr />
<div>Here's a list of courses with useful online materials:<br />
<br />
== Courses ==<br />
* [[PChemFall2019| USF Physical Chemistry I (2019)]]<br />
* [[Courses/PChemSpring2019 | USF Physical Chemistry II (2019)]]<br />
* [[PChemFall2018| USF Physical Chemistry I (2018)]]<br />
* [[PChemFall2017| USF Physical Chemistry I (2017)]]<br />
* [[PChemFall2016| USF Physical Chemistry I (2016)]]<br />
* [[GradQuantumFall2013| USF Graduate Quantum Mechanics I]]<br />
* [[GradQuantumSpring2014| USF Graduate Quantum Mechanics II]]<br />
* [[CompSciSpring2018|Introduction to Scientific Computing (2018)]]<br />
* [[CompSciSpring2017|Introduction to Scientific Computing (2017)]]<br />
* [[CompSciSpring2016|Introduction to Scientific Computing (2016)]]<br />
* [[CompSciFall2014|Introduction to Scientific Computing (2014)]]<br />
* [http://lambda-the-ultimate.org/classic/Courses.html Functional Programming]<br />
<br />
== Lecture Series ==<br />
* [http://www.esqc.org/lectures European Summer School in Quantum Chemistry]<br />
<br />
== Tutorials ==<br />
* [[HowTo:Fourier|Fourier transforms]]<br />
* [http://www.mathematica-journal.com/2012/02/evaluation-of-gaussian-molecular-integrals Evaluating Matrix Elements]<br />
* [http://www.haskell.org/tutorial/ Haskell]<br />
* [http://monads.haskell.cz/html/index.html Monads]<br />
* [http://www.yosefk.com/blog/my-history-with-forth-stack-machines.html The Forth Language]<br />
<br />
== Reference Material ==<br />
* [http://dft.sandia.gov/Quest/DFT_codes.html List of DFT Codes]<br />
* [http://docs.python.org/3/tutorial/ Python Tutorial]<br />
* [http://www.nwchem-sw.org/index.php/Release62:NWChem_Documentation NWChem Documentation]<br />
* [http://www.ebi.ac.uk/pdbe-srv/pdbechem/ PDB Ligand Structures]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Main_Page&diff=753Main Page2019-09-10T17:55:10Z<p>David M. Rogers: </p>
<hr />
<div>Welcome to the David M. Rogers' research group in Multiscale Chemical Physics at the University of South Florida.<br />
<br />
We develop predictive models for new physics and chemistry that appear<br />
when moving up from the atomic to the nano and micro-scale. To support this<br />
goal, we are developing the thermodynamics of far-from equilibrium systems,<br />
building functional data structures for supercomputing and applying Bayesian<br />
inference to mine simulation data. Work in these topics builds on recent<br />
advances in fundamental computer science, applied statistics, and<br />
nonequilibrium physics and chemistry. Together, new developments in these<br />
fields will allow unprecedented access to electron through device-level<br />
simulations and analysis for materials design grounded in fundamental physics.<br />
<br />
Two research areas collectively have the potential to<br />
greatly reduce the time and effort building, running, and analyzing<br />
molecular and continuum simulations for modern high-performance<br />
computing platforms.<br />
The first expands the theory and techniques of statistical<br />
mechanics for probabilistic simulation of energy conversion<br />
devices. The second applies advances in domain-specific languages<br />
to eliminate the lag between defining a physical, Hamiltonian model and carrying<br />
out dynamics and other computations on its potential energy<br />
landscape.<br />
<br />
For more details, see the [[Research]], [[Publications]], and [[Predictive_Chemistry:Current_events|Current events]] links.</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=PChemFall2019&diff=752PChemFall20192019-08-19T17:28:24Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry I</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4410-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Aug. 27 - Nov. 26, 2019<br />
* Meeting Times: Tues. and Thurs., 3:30-4:45 pm in CIS 3064<br />
** Regular quizzes on Tuesdays<br />
** Problem Sessions: Fri., 2-2:50 pm in CIS 3064<br />
** Office Hours: by request and TBA<br />
<br />
* Grading:<br />
** Quiz (25%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (25%) Thurs., Sept. 26 3:30-4:45 pm (CIS 3064)<br />
** Exam 2 (25%) Thurs., Oct. 24 3:30-4:45 pm (CIS 3064)<br />
** Final (25%) due Tues., Nov. 26 3:30 pm (Canvas or CIS 3064)<br />
<br />
== Overview ==<br />
<br />
This is the first part of a 2-semester course in thermodynamics. This course will cover the mathematical theory of chemical equilibrium, heat, and work. These are the driving forces behind the operation of Le Châtelier's principle, and are routinely used to understand and control chemical reactions, states of matter, and amount and efficiency of energy production.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
<br />
== Resources ==<br />
<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/ktcon.html Kinetic Theory] at HyperPhysics<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html Heat Concepts] at HyperPhysics<br />
** Note: McQuarrie says dU = dQ + dW, while Nave says dU = dQ - dW. There is no contradiction, since McQuarrie's dW = -P dV (work done on the system), while Nave's dW = P dV (work done by the system). I prefer the first definition.<br />
* News from the frontlines of exploring entropy: [http://scitation.aip.org/content/aip/magazine/physicstoday/article/68/9/10.1063/PT.3.2912 Information: From Maxwell’s demon to Landauer’s eraser]<br />
* [[Media:Transforms.pdf|Notes]] on transformations of variables.<br />
* [[PChemFall2018 | Course Page from 2018]]<br />
* [[PChemFall2017 | Course Page from 2017]]<br />
* [[PChemFall2016 | Course Page from 2016]]<br />
* [[PChemFall2015 | Course Page from 2015]] -- contains previous quizzes and keys.<br />
* [https://predictivestatmech.org/papers/quiz0.pdf Pretest key]<br />
* [https://predictivestatmech.org/papers/quiz1_2018.pdf Quiz 1 Key] -- for more information and practice problems, see The Vallance Chemistry Group, U. Oxford (http://vallance.chem.ox.ac.uk under Teaching -> Units and Dimensions).<br />
* Gas Thermodynamics Videos:<br />
** P-V work demonstrated by a [https://youtu.be/j0TQxYemrgg?t=75 Steel Drum Implosion]<br />
** Adiabatic Compression in a [https://youtu.be/4qe1Ueifekg?t=144 Fire Piston]<br />
** Complete thermodynamic cycle [https://youtu.be/EtF3-YmHp_0?t=29 Stirling Engine]<br />
** Pressure (concentration gradient) driven chemical work [https://youtu.be/3y1dO4nNaKY?t=95 ATP Synthetase]<br />
<br />
== Topics ==<br />
<br />
# Moving Freely in P-V-T space (Chapter H, with examples from Ch. 16-[2,3,5,6,7], 17-[4,5], and 19-1)<br />
#* Isobaric, isothermal, and isochoric processes<br />
#* State functions<br />
#* Implicit, partial, and total derivatives<br />
#* Integration along a path<br />
#* Relations between partial derivatives<br />
#** Transformations using substitution<br />
#** Transformations using the chain rule<br />
#* Visualizing isosurfaces<br />
#* Using P(V,T) / V(P,T) / T(P,V)<br />
# First Law of Thermodynamics – conserved quantities (Ch. 19-[2 to 9])<br />
#* Mechanisms of energy flow: work, heat, mass/chemical<br />
#* Integrating work and heat for common processes<br />
#* Energy of a molecule vs. a collection – translation, rotation, intermolecular, etc.<br />
#* Extensive and intensive quantities<br />
#* Using energy balance for fun and profit.<br />
# Standard States and Energies (Ch. 19-[10,11,12], Ch 26-[3,6,7,8,9])<br />
#* Connecting to analytical chemistry.<br />
#* Spontaneous, irreversible, processes vs. quasistatic processes.<br />
#* Experimentally measuring reaction constants and heats. (Ch. 21-5)<br />
# The Second Law of Thermodynamics: Energy, Enthalpy, Entropy, and Free Energy (Ch. 20)<br />
#* The absolute temperature scale. (Ch. 16-1)<br />
#* Inequalities followed by each path type. (Ch. 22-[1,2])<br />
#* Heat, measurement, information, Maxwell’s demon and Landauer’s principle.<br />
# Basic Probability<br />
#* Simple counting (Ch. J)<br />
#* Velocity distribution function (Ch 27-[1,2,3,4])<br />
#* Boltzmann distributions (Ch. 17-[1,2,3,6 to 8])<br />
# Applications:<br />
#* Quantitative Prediction of Reaction Equilibria (Ch. 26)<br />
#* Liquid solutions: osmotic pressure, vapor pressure, Henry’s and Raoult’s Laws (Ch. 24)<br />
#* Phase Equilibria and Basic Phase Diagrams (Ch. 23)<br />
#* Thermodynamic Cycles, Examples with Refrigeration and Galvanic Cell (Ch. 20-7)<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Moving Freely in P-V-T space<br />
#* H: 1-5,7,10-14<br />
#* 16:1-21,25,26(1st part),29,35-42,44-45,52-56,58-59,33(optional)<br />
#** sketch a plot for 16.4 and 16.5<br />
#* 17: 9-17<br />
# First Law (sec. 19-1 through 19-9)<br />
#* 19:1-31<br />
#* You can skip 19-27 and 28 (we'll do in class)<br />
# Standard States and Energies (sec. 19-10 through 19-12, 21-5 and 26-3 through 26-9)<br />
#* 19:34-49<br />
#* 21: 1-7, 10-26, 29, 48, 42-43, 45-47<br />
#* 26: 2,6,8-11,13,16-17,21<br />
#* 26: 61 -- only integrate dG = V dP at constant V=1/rho.<br />
# Entropy, Free Energy and the Second Law (all of Ch. 20, sections 16:1, 22:1-2)<br />
#* 20: 2-4, 6-16, 18-19, 24-25, 27-30, 32-33<br />
#* 22: 1-5 (for 4 and 5 use 1st law and Gibbs relation from A)<br />
#* 16: 4,6-11<br />
# Basic Probability (Ch. J, 17 and 27)<br />
#* J: 1-7<br />
#* 17: 1, 3, 4, 7-8 [for 7, use a 3-state system with E(0) = 0, E(-1) = -1, E(1) = 1]<br />
#* 27:1-9<br />
# Applications:<br />
## Reaction Equilibria (Ch. 26)<br />
##* 26: 3-7, 12, 14-15, 33, 59, 61, 62-65<br />
## Phase Equilibria and Basic Phase Diagrams (Ch. 23)<br />
## Liquid Solutions: Osmotic Pressure, Henry's and Raoult's Law (Ch. 24)<br />
<br />
== Online Tutorials ==<br />
<br />
There are some excellent introductory videos on Khan Academy that are useful if you need a refresher or extra practice with some of the topics in the course.<br />
<br />
# Moving Freely in P-V-T space<br />
#* Isobars & Work [https://www.khanacademy.org/test-prep/mcat/chemical-processes/thermodynamics-mcat/v/pv-diagrams-part-1-work-and-isobaric-processes]<br />
#* Isotherms, Isochors, Adiabats [https://www.khanacademy.org/test-prep/mcat/chemical-processes/thermodynamics-mcat/v/pv-diagrams-part-2-isothermal-isometric-adiabatic-processes]<br />
#* Implicit Derivatives (explained with practice problems) [https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-implicit-diff/v/implicit-differentiation-1]<br />
#* Partial Derivatives (explained with practice problems) [https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivatives/v/partial-derivatives-introduction]<br />
#* State Functions (Macrostates vs Microstates) [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/macrostates-and-microstates]<br />
#* Quasistatic and Reversible Processes [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/quasistatic-and-reversible-processes]<br />
#* Integration along a path (using PV-diagrams and expansion/compression Work) [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/pv-diagrams-and-expansion-work]<br />
# First Law of Thermodynamics – conserved quantities (Ch. 19-[2 to 9])<br />
#* PV work [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/a/pressure-volume-work]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=PChemFall2019&diff=751PChemFall20192019-08-19T17:27:24Z<p>David M. Rogers: Created page with "'''<BIG>Physical Chemistry I</BIG>''' Course Info * Course Numbers CHM 4410-001 * Credit Hours: 4 * Meeting Dates: Aug. 27 - Nov. 26, 2018 * Meeting Times: Tues. and Thurs.,..."</p>
<hr />
<div>'''<BIG>Physical Chemistry I</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4410-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Aug. 27 - Nov. 26, 2018<br />
* Meeting Times: Tues. and Thurs., 3:30-4:45 pm in CIS 3064<br />
** Regular quizzes on Tuesdays<br />
** Problem Sessions: Fri., 2-2:50 pm in CIS 3064<br />
** Office Hours: by request and TBA<br />
<br />
* Grading:<br />
** Quiz (25%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (25%) Thurs., Sept. 26 3:30-4:45 pm (CIS 3064)<br />
** Exam 2 (25%) Thurs., Oct. 24 3:30-4:45 pm (CIS 3064)<br />
** Final (25%) due Tues., Nov. 26 3:30 pm (Canvas or CIS 3064)<br />
<br />
== Overview ==<br />
<br />
This is the first part of a 2-semester course in thermodynamics. This course will cover the mathematical theory of chemical equilibrium, heat, and work. These are the driving forces behind the operation of Le Châtelier's principle, and are routinely used to understand and control chemical reactions, states of matter, and amount and efficiency of energy production.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
<br />
== Resources ==<br />
<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/ktcon.html Kinetic Theory] at HyperPhysics<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html Heat Concepts] at HyperPhysics<br />
** Note: McQuarrie says dU = dQ + dW, while Nave says dU = dQ - dW. There is no contradiction, since McQuarrie's dW = -P dV (work done on the system), while Nave's dW = P dV (work done by the system). I prefer the first definition.<br />
* News from the frontlines of exploring entropy: [http://scitation.aip.org/content/aip/magazine/physicstoday/article/68/9/10.1063/PT.3.2912 Information: From Maxwell’s demon to Landauer’s eraser]<br />
* [[Media:Transforms.pdf|Notes]] on transformations of variables.<br />
* [[PChemFall2017 | Course Page from 2017]]<br />
* [[PChemFall2016 | Course Page from 2016]]<br />
* [[PChemFall2015 | Course Page from 2015]] -- contains previous quizzes and keys.<br />
* [https://predictivestatmech.org/papers/quiz0.pdf Pretest key]<br />
* [https://predictivestatmech.org/papers/quiz1_2018.pdf Quiz 1 Key] -- for more information and practice problems, see The Vallance Chemistry Group, U. Oxford (http://vallance.chem.ox.ac.uk under Teaching -> Units and Dimensions).<br />
* Gas Thermodynamics Videos:<br />
** P-V work demonstrated by a [https://youtu.be/j0TQxYemrgg?t=75 Steel Drum Implosion]<br />
** Adiabatic Compression in a [https://youtu.be/4qe1Ueifekg?t=144 Fire Piston]<br />
** Complete thermodynamic cycle [https://youtu.be/EtF3-YmHp_0?t=29 Stirling Engine]<br />
** Pressure (concentration gradient) driven chemical work [https://youtu.be/3y1dO4nNaKY?t=95 ATP Synthetase]<br />
<br />
== Topics ==<br />
<br />
# Moving Freely in P-V-T space (Chapter H, with examples from Ch. 16-[2,3,5,6,7], 17-[4,5], and 19-1)<br />
#* Isobaric, isothermal, and isochoric processes<br />
#* State functions<br />
#* Implicit, partial, and total derivatives<br />
#* Integration along a path<br />
#* Relations between partial derivatives<br />
#** Transformations using substitution<br />
#** Transformations using the chain rule<br />
#* Visualizing isosurfaces<br />
#* Using P(V,T) / V(P,T) / T(P,V)<br />
# First Law of Thermodynamics – conserved quantities (Ch. 19-[2 to 9])<br />
#* Mechanisms of energy flow: work, heat, mass/chemical<br />
#* Integrating work and heat for common processes<br />
#* Energy of a molecule vs. a collection – translation, rotation, intermolecular, etc.<br />
#* Extensive and intensive quantities<br />
#* Using energy balance for fun and profit.<br />
# Standard States and Energies (Ch. 19-[10,11,12], Ch 26-[3,6,7,8,9])<br />
#* Connecting to analytical chemistry.<br />
#* Spontaneous, irreversible, processes vs. quasistatic processes.<br />
#* Experimentally measuring reaction constants and heats. (Ch. 21-5)<br />
# The Second Law of Thermodynamics: Energy, Enthalpy, Entropy, and Free Energy (Ch. 20)<br />
#* The absolute temperature scale. (Ch. 16-1)<br />
#* Inequalities followed by each path type. (Ch. 22-[1,2])<br />
#* Heat, measurement, information, Maxwell’s demon and Landauer’s principle.<br />
# Basic Probability<br />
#* Simple counting (Ch. J)<br />
#* Velocity distribution function (Ch 27-[1,2,3,4])<br />
#* Boltzmann distributions (Ch. 17-[1,2,3,6 to 8])<br />
# Applications:<br />
#* Quantitative Prediction of Reaction Equilibria (Ch. 26)<br />
#* Liquid solutions: osmotic pressure, vapor pressure, Henry’s and Raoult’s Laws (Ch. 24)<br />
#* Phase Equilibria and Basic Phase Diagrams (Ch. 23)<br />
#* Thermodynamic Cycles, Examples with Refrigeration and Galvanic Cell (Ch. 20-7)<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Moving Freely in P-V-T space<br />
#* H: 1-5,7,10-14<br />
#* 16:1-21,25,26(1st part),29,35-42,44-45,52-56,58-59,33(optional)<br />
#** sketch a plot for 16.4 and 16.5<br />
#* 17: 9-17<br />
# First Law (sec. 19-1 through 19-9)<br />
#* 19:1-31<br />
#* You can skip 19-27 and 28 (we'll do in class)<br />
# Standard States and Energies (sec. 19-10 through 19-12, 21-5 and 26-3 through 26-9)<br />
#* 19:34-49<br />
#* 21: 1-7, 10-26, 29, 48, 42-43, 45-47<br />
#* 26: 2,6,8-11,13,16-17,21<br />
#* 26: 61 -- only integrate dG = V dP at constant V=1/rho.<br />
# Entropy, Free Energy and the Second Law (all of Ch. 20, sections 16:1, 22:1-2)<br />
#* 20: 2-4, 6-16, 18-19, 24-25, 27-30, 32-33<br />
#* 22: 1-5 (for 4 and 5 use 1st law and Gibbs relation from A)<br />
#* 16: 4,6-11<br />
# Basic Probability (Ch. J, 17 and 27)<br />
#* J: 1-7<br />
#* 17: 1, 3, 4, 7-8 [for 7, use a 3-state system with E(0) = 0, E(-1) = -1, E(1) = 1]<br />
#* 27:1-9<br />
# Applications:<br />
## Reaction Equilibria (Ch. 26)<br />
##* 26: 3-7, 12, 14-15, 33, 59, 61, 62-65<br />
## Phase Equilibria and Basic Phase Diagrams (Ch. 23)<br />
## Liquid Solutions: Osmotic Pressure, Henry's and Raoult's Law (Ch. 24)<br />
<br />
== Online Tutorials ==<br />
<br />
There are some excellent introductory videos on Khan Academy that are useful if you need a refresher or extra practice with some of the topics in the course.<br />
<br />
# Moving Freely in P-V-T space<br />
#* Isobars & Work [https://www.khanacademy.org/test-prep/mcat/chemical-processes/thermodynamics-mcat/v/pv-diagrams-part-1-work-and-isobaric-processes]<br />
#* Isotherms, Isochors, Adiabats [https://www.khanacademy.org/test-prep/mcat/chemical-processes/thermodynamics-mcat/v/pv-diagrams-part-2-isothermal-isometric-adiabatic-processes]<br />
#* Implicit Derivatives (explained with practice problems) [https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-implicit-diff/v/implicit-differentiation-1]<br />
#* Partial Derivatives (explained with practice problems) [https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivatives/v/partial-derivatives-introduction]<br />
#* State Functions (Macrostates vs Microstates) [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/macrostates-and-microstates]<br />
#* Quasistatic and Reversible Processes [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/quasistatic-and-reversible-processes]<br />
#* Integration along a path (using PV-diagrams and expansion/compression Work) [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/v/pv-diagrams-and-expansion-work]<br />
# First Law of Thermodynamics – conserved quantities (Ch. 19-[2 to 9])<br />
#* PV work [https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/a/pressure-volume-work]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Publications&diff=750Publications2019-08-19T12:52:05Z<p>David M. Rogers: </p>
<hr />
<div>{| cellpadding="4" style="border: 1px solid darkgray;"<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Unifying theories for nonequilibrium statistical mechanics."<br />
[https://dx.doi.org/10.1088/1742-5468/ab3193 J. Stat. Mech. 084010, 2019].<br />
<br />
One of my longest-running projects is finally published. Large deviation functions calculated from "experimental" simulations of two model systems illustrate the key ideas of maximum transition entropy - a refinement of Jaynes' maximum caliber that preserves causality.<br />
|- style="border: 1px solid darkgray;"<br />
|| Guy W. Dayhoff II and David M. Rogers, "Hydration and Dispersion Forces in Hydroxypropylcellulose Phase Behavior." [https://dx.doi.org/10.1021/acs.jpcb.9b01049 J. Phys. Chem B in press, 2019].<br />
<br />
We extend four forcefields to model hydroxypropylcellulose and find that none of them can reproduce experimentally measured hydration forces from 2001. Long-range solvent-mediated forces remain challenging targets for predictive simulation because of a breakdown in science funding priorities.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Range separation: The divide between local structures and field theories." [https://dx.doi.org/10.13128/Substantia-208 Substantia 3(1), 2019].<br />
<br />
This work presents parallel histories of the development of two modern theories of condensed matter: the theory of electron structure in quantum mechanics, and the theory of liquid structure in statistical mechanics. Key developments provide some guidance on important directions for future advancements in theory and practice.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Dual Characterization of the Ornstein-Zernike Equation in Moment Space." [https://arxiv.org/abs/1807.05963 submitted, 2019].<br />
<br />
I re-write Ornstein-Zernike theory in a convenient matrix basis so that future computational implementations can be made robust and that numerical and fitting error can be tightly controlled. It is hoped that the framework can be used in the near future to compute molecular solvation free energies and to realize its enormous potential economic and environmental benefits for formulating industrial fluids and consumer products.<br />
|- style="border: 1px solid darkgray;"<br />
|| Phillip S. Hudson, Stefan Boresch, David M. Rogers, and H. Lee Woodcock., "Accelerating QM/MM Free Energy Computations via Intramolecular Force Matching" [https://dx.doi.org/10.1021/acs.jctc.8b00517 J. Chem. Theory Comput., 14 (12):6327–35, 2018].<br />
<br />
My co-authors apply [https://github.com/frobnitzem/chemparam my algorithm and software implementation of Bayesian generalized linear model regression with linear inequality constraints] to estimate molecular modeling parameters from quantum their mechanical calculations. They find the method gives robust results that greatly increase efficiency of additional simulations.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Extension of Kirkwood-Buff theory to the canonical ensemble." [https://aip.scitation.org/doi/full/10.1063/1.5011696 J. Chem. Phys., 148:054102, 2018].<br />
<br />
We present a way to utilize Essmann et. al.'s smooth particle mesh Ewald algorithm ([https://github.com/frobnitzem/EwaldCorrel implemented here]) to get the low-angle direct correlation function from canonical ensemble simulation data. The result avoids well-documented issues with long wavelength (small-angle scattering) modes that appear when using real-space methods. This result is combined with new estimates of finite-size effects and grand-canonical ensemble corrections to provide definitive results on the problem of extrapolating Kirkwood-Buff integrals.<br />
|- style="border: 1px solid darkgray;"<br />
|| Juan M. Vanegas, Frank Heinrich, David M.Rogers, Bryan D. Carson, Sadie La Bauve, Briana C. Vernon, Bulent Akgun, Sushil Satija, Aihua Zheng, Margaret Kielian, Susan B. Rempe, and Michael S. Kent, "Insertion of Dengue E into lipid bilayers studied by neutron reflectivity and molecular dynamics simulations." [https://authors.elsevier.com/c/1WcOv1ClS9Jvp BBA 1860(5):1216-1230, 2018].<br />
<br />
We compare neutron reflectivity experiments to molecular dynamics calculations on the orientation and binding position<br />
of the Dengue envelope protein responsible for viral escape from the host cell's endosome. In addition to the hydrophobic fusion tip, we find important roles for three positively-charged residues in the viral protein that contribute to host membrane binding. These could potentially be targeted by new anti-viral medicines.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "An information theory model for dissipation in open quantum systems." [http://iopscience.iop.org/article/10.1088/1742-6596/880/1/012039 J. Phys., Conference Series 880(1):012039, 2017].<br />
<br />
This paper presents a new, simple ansatz for adding dissipation to arbitrary stochastic forcing of a quantum dynamical system.<br />
For Gaussian random forces, it predicts a Lindblad equation identical to the Caldeira-Leggett model <br />
up to order <math>\beta^2</math>, where the same term is present with a different prefactor.<br />
The system-centric, phase space picture here shows that the <math>\beta^2</math> term represents<br />
a quantum confinement effect.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Einstein-Podolsky-Rosen paradox implies a minimum achievable temperature." [http://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.012149 Phys. Rev. E 95, 012149, 2017.]<br />
<br />
This paper provides measurement-based definitions of heat and work that can be realized in current laboratory setups.<br />
The first and second laws are proved despite the fact that temperature is treated completely as as a property of the interacting reservoir. Measurements of the work are subject to the famous EPR paradox because the work exchanged between two quantum systems is not defined until a measurement is performed. Based on this, we show that even an environment at absolute zero cannot lower a system's temperature below a minimum characteristic of the way the environment is coupled to the system.<br />
|- style="border: 1px solid darkgray;"<br />
|| Guy W. Dayhoff II and David M. Rogers, "Driving forces in MD simulations of transition and ‘Free’ flows." [http://dx.doi.org/10.1080/08927022.2016.1273524 Mol. Sim. 43(5-6), pp. 467-477, 2017.] (special issue on Surface Chemistry)<br />
<br />
We set out to test the Joule-Thomson analysis of thermodynamics of porous flow for gasses through a nanopore and found that while local equilibrium is established in the steady-state, finite-size effects cause heat flow opposite the flow direction that violates the assumption of an adiabatic porous plug.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Efficient Primitives for Standard Tensor Linear Algebra." [https://doi.org/10.1145/2949550.2949580 Proc. XSEDE16 Conference on Diversity, Big Data, and Science at Scale, no. 14, 2016.]<br />
<br />
This paper introduces 3 basic functions that generalize BLAS to tensors and presents a code generation strategy for their [https://github.com/frobnitzem/slack efficient execution on GPUs] that achieves peak performance on the same order of magnitude as for traditional, vendor-optimized matrix-multiplications.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Overcoming the Minimum Image Constraint Using the Closest Point Search." [http://dx.doi.org/10.1016/j.jmgm.2016.07.004 J. Mol. Graph. Model 68, pp. 197–205, 2016.]<br />
<br />
An elegant solution to the problem of finding periodic images in non-rectangular lattices is provided based on the closest vector problem. Related code is here: [https://github.com/frobnitzem/pbctools]<br />
|- style="border: 1px solid darkgray;"<br />
|| Elisa La Bauve, Briana C. Vernon, Dongmei Ye, David M. Rogers, Cathryn M. Siegrist, Bryan Carson. Susan L. Rempe, Aihua Zheng, Margaret C. Kielian, Andrew P. Shreve, and Michael S. Kent. "Method for measuring the unbinding energy of strongly-bound membrane-associated proteins." [http://dx.doi.org/10.1016/j.bbamem.2016.07.004 BBA Biomembranes 1858(11): 2753–62, 2016.]<br />
<br />
This paper gives multiple experimental measurements of binding energy between the Dengue virus envelope protein<br />
and host membranes that largely confirm our computational predictions from 2015.<br />
I contributed all the theory for terminal velocity during sedimentation, along with a novel kinetic analysis providing the free energy and enthalpy of the dissociation barrier (all the details are at the end of the appendix).<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Thermodynamics of Maximum Transition Entropy for Quantum Assemblies." [http://arxiv.org/abs/1503.01232 arXiv:1503.01232 submitted, 2016].<br />
<br />
The work presents a new, general, theoretical foundation for the dynamics of open quantum systems modeled on the maximum entropy derivation of equilibrium statistical mechanics. Computational results are presented for three detailed systems to validate and reinforce the theory. It represents a significant advancement for the field, as it lucidly connects the dynamics of a single wavefunction plus environmental noise to the Caldeira-Leggett model for density matrices.<br />
|- style="border: 1px solid darkgray;"<br />
|| Andriy Anishkin, Juan M. Vanegas, David M. Rogers, Philip L. Lorenzi, Wai Kin Chan, Preeti Purwaha, John N. Weinstein, Sergei Sukharev, and Susan B. Rempe. "Catalytic Role of the Substrate Defines Specificity of Therapeutic L-Asparaginase."<br />
[http://dx.doi.org/10.1016/j.jmb.2015.06.017 J. Mol. Biol. 427:2867-2885, 2015].<br />
<br />
We present an explanation for the (until now controversial) catalytic mechanism of type 2 bacterial L-asparaginase enzymes.<br />
By using the carboxylic acid of the substrate (asparagine) as the proton acceptor, this enzyme is able to preferentially carry out deamidation on asparagine more quickly than for the competing substrate, glutamine. The hypothesis, re-discovered from our MD simulations, was first put forward years ago in contested experimental studies, and now finds additional support from our MD and QM calculations.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Towards a Direct, By-Need Evaluator for Dependently Typed Languages."<br />
[http://arxiv.org/abs/1509.07036 arXiv:1509.07036 submitted, 2015].<br />
<br />
This paper describes the implementation of a new interpreted language for distributed parallel computing.<br />
It achieves its goal by maintaining pure functional semantics,<br />
allowing all terms in the language to be partially evaluated and serialized to network storage<br />
at any point during computation.<br />
|- style="border: 1px solid darkgray;"<br />
|| Marielle Soniat, David M. Rogers, and Susan Rempe. "Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration." [http://pubs.acs.org/doi/abs/10.1021/acs.jctc.5b00357 J. Chem. Theory. Comput. 142:074101, 2015].<br />
<br />
We studied the influence of dispersion energy corrections on the free energy of formation for sodium-water clusters computed with DFT and wound up discovering that dispersion and split-range exchange functionals can somewhat counter-balance each other. The charged sodium ion pulls on the water's electrons, clearly showing which density functionals over-polarize compared to CCSD. Split-range exchange can reduce this over-polarization, but results in reduced electrostatic interaction. Dispersion can lower the binding energy again to counter-balance. So, functionals fit to experimental formation energies need both effects to avoid lowering energies by over-polarizing.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Real-space quadrature: a convenient, efficient representation for multipole expansions." [http://dx.doi.org/10.1063/1.4907404 J. Chem. Phys. 142:074101, 2015]. ([http://predictivestatmech.org/papers/real-poles.pdf Presentation])<br />
<br />
I introduce sets of point charges that are able to simultaneously reproduce all multipole (spherical harmonic) expansions up to arbitrary order. The number of points is space-optimal. Translations are described from the usual harmonics and from Cartesian moments (dipole, quadrupole, etc.) on supersymmetric tensors to directional moments using the point weight distribution. Many applications are possible, including trivial implementation of multipoles in molecular mechanics and representing probability distributions over rotation space.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Michael S. Kent, and Susan B. Rempe, "Molecular basis of endosomal-membrane association for the dengue virus envelope protein." [http://dx.doi.org/10.1016/j.bbamem.2014.12.018 BBA Biomembranes 1848(4):1041-52, 2015.]<br />
<br />
A fully atomistic potential of mean force for association of the viral envelope protein from Dengue virus was compared to a Poisson-Boltzmann electrostatic plus dispersion model. The results are consistent, showing hope for this type of combined scale simulation.<br />
|- style="border: 1px solid darkgray;"<br />
|| Yaqin Fu, Binsong Li, Ying-Bing Jiang, Darren R. Dunphy, Andy Tsai, Siu-Yue Tam, Hongyou Fan, Hongxia Zhan, David Rogers, Susan Rempe, Plamen Atanassov, Joseph L. Cecchi, and C. Jeffrey Brinker "Atomic Layer Deposition of L-Alanine Polypeptide." [http://pubs.acs.org/doi/abs/10.1021/ja5043403 JACS 136(45):15821–4, 2014.]<br />
<br />
This paper with our experimental collaborators carried out blocked peptide synthesis by vapor-depositing Boc-L-alanine to create a uniform thin film of polypeptides grown on a silica substrate activated by aminopropyltrimethoxysilane.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Silmaril, A Functional Language for Distributed Parallel Evaluation." [http://predictivestatmech.org/sil/papers/sil.pdf Submitted version]<br />
|- style="border: 1px solid darkgray;"<br />
|| Mathias B. Andersen, David M. Rogers, Junyu Mai, Benjamin Schudel, Anson V. Hatch, Susan B. Rempe and Ali Mani. "Spatiotemporal pH dynamics in concentration polarization near ion-selective membranes." [http://dx.doi.org/10.1021/la5014297 Langmuir, 30(26):7902–7912, 2014]<br />
|- style="border: 1px solid darkgray;"<br />
|| W. K. Chan, P. L. Lorenzi, A. Anishkin, P. Purwaha, D. M. Rogers, S. Sukharev, S.B. Rempe, and J. N. Weinstein. "The glutaminase activity of l-asparaginase is not required for anticancer activity against ASNS-negative cells." [http://dx.doi.org/10.1182/blood-2013-10-535112 Blood. 123(23):3596-606, 2014].<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Dian Jiao, Lawrence Pratt, and Susan B. Rempe. "Structural Models and Molecular Thermodynamics of Hydration of Ions and Small Molecules" [http://dx.doi.org/10.1016/B978-0-444-59440-2.00004-1 Annu. Rep. Comp. Chem. 8:71–127, 2012.]<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Susan B. Rempe. "Irreversible Thermodynamics." [http://dx.doi.org/10.1088/1742-6596/402/1/012014 J. Phys.: Conf. Ser. 402:012014, 2012].<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Thomas L. Beck, and Susan B. Rempe. [[Media:Dmroge_InfoNonequ2011.pdf|"An Information Theory Approach to Nonlinear, Nonequilibrium Thermodynamics."]] [http://dx.doi.org/10.1007/s10955-011-0358-9 J. Stat. Phys. 145(2):385-409, 2011]<br />
<br />
We show how the interpretation of thermodynamic states as representing system information leads naturally to thermodynamic cycles and the first and second laws of thermodynamics as well as similar formulations for nontrivial nonequilibrium problems. The logical development of the theory also leads naturally to correct indistinguishability factors in the partition function.<br />
|- style="border: 1px solid darkgray;"<br />
|| Sameer Varma, David M. Rogers, Lawrence R. Pratt, and Susan B. Rempe. "Perspectives on Ion Selectivity: Design Principles for K+ Selectivity in Membrane Transport." [http://jgp.rupress.org/content/137/6/479.full J. Gen. Physiol., 137(6):479-488, 2011.]<br />
<br />
We review the development of models for understanding the physical basis of selectivity for K+ ions over Na+, its sibling only one row behind, in membrane channels and transporters. Although the problem is subtle because of the morass of competing effects, we emphasize work analyzing the systematic influence of the environment on tipping local binding site structure toward selective configurations.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Susan B. Rempe. [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3443978/ “Probing the Thermodynamics of Competitive Ion Binding Using Minimum Energy Structures.”] [http://dx.doi.org/10.1021/jp2012864 J. Phys. Chem. B, 115(29):9116-29, 2011].<br />
<br />
We presented an extension of the Quasi-Chemical theory for quantifying the impact of local structure on ion complexation thermodynamics. The theory can be simply represented using a set of thermodynamic cycles involving binding site structural and compositional states as reaction intermediates.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| Susan B. Rempe and David M. Rogers; et. al. “Computational and experimental platform for understanding and optimizing water flux and salt rejection in nanoporous membranes.” [http://prod.sandia.gov/techlib/access-control.cgi/2010/106735.pdf Sandia Technical Report, SAND2010-6735, 2010.]<br />
<br />
We summarize work on designing polymer coatings for salt exclusion in water transporting nanopores. In this work, I collected available molecular dynamics results for these systems and performed a novel energy efficiency analysis able to relate atomistic and experimental scales as well as identify important design goals and chemical principles for material performance.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, [http://rave.ohiolink.edu/etdc/view?acc_num=ucin1251832030 ''''Using Bayes' Theorem for Free Energy Calculations''''], 2009.<br />
<br />
We investigated the central quantity of free energies in a Bayesian context and provide estimators for solvation free energies as well as optimal potential of mean force approximations to model polymer coarse-grained dynamics from atomistic simulations.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| Zhen Zhao, David M. Rogers and Thomas L. Beck. "Polarization and Charge Transfer in the Hydration of Chloride Ions." [http://link.aip.org/link/?JCP/132/014502/1 J. Chem. Phys., 132:014502, 2010.]<br />
<br />
Dr. Zhao's ab-initio analysis of the charge distribution in water-ion clusters highlighted the importance of many-body water-water interactions and charge transfer effects in determining cluster structural and energetic properties. These are still challenging to represent in modern polarizable forcefields and have implications for anion properties at interfaces.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Quasi-Chemical and Structural Analysis of Polarizable Anion Hydration." [http://link.aip.org/link/?JCP/132/014505/1 J. Chem. Phys., 132:014505, 2010.]<br />
<br />
The role of polarizability in forcefield-based models of ions and water was examined. Utilizing some of our recent developments on quasi-chemical theory, we have been able to quantify the tightened, asymmetric nature of the ion's local solvation waters induced by increased polarizability as well as the exact effects of polarization on the solvation free energy. The results suggest some potential problems and diagnostics for such models.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. [http://forcesolve.sourceforge.net/ Force Solve] (Sourceforge, Chicago IL, 2008).<br />
<br />
This force matching software implements and tests coarse-graining for general molecular systems in a mere 4000 lines of code. It is able to parametrize coarse Hamiltonians from atomic trajectory data given arbitrary definitions of coarse united-atom type models as well as carry out short Langevin Dynamics simulations on the coarse scale. The program's main drawbacks are its slow speed and high memory usage due to its simplistic design, attributable to the interpreted nature of python.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Resolution and Scale Independent Nonparametric Function Matching Using a String Energy Penalized Spline Prior." 2008. [http://arxiv.org/abs/1003.4741 arXiv:1003.4741v1] (stat.ML).<br />
<br />
Fresh insight is provided into long-standing mathematical issues surrounding computational modeling of continuous functions from a few sampled data points. The present research lays the groundwork for predicting the behavior of complicated many-body systems using advanced regression techniques.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Modeling molecular and ionic absolute solvation free energies with quasichemical theory bounds." [https://doi.org/10.1063/1.2985613 J. Chem. Phys., 129:134505, 2008.]<br />
<br />
We develop a Bayesian method for computing (with error bars) the free energy for forming a nano-bubble in an arbitrary solvent system. This forms the first step of a thermodynamic cycle for dissolving a real solute. We prove that upper and lower bounds for that solvation free energy can be obtained from two simulations (with and without the solute present). The method is excellent for dissolving gas in water, while the upper/lower bounds are larger for dissolving water or ions.<br />
|}<br />
<br />
== Manuscripts in Preparation/Submitted ==<br />
* [https://arxiv.org/abs/1712.09427 Fluctuation Theory of Ionic Solvation Potentials]<br />
* [https://arxiv.org/abs/1503.01232 Thermodynamics of Maximum Transition Entropy for Quantum Assemblies]<br />
* [https://arxiv.org/abs/1701.01466 Maximum Entropy Closure for Flows in Transiently Driven Nonequilibrium Systems]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Publications&diff=749Publications2019-05-30T21:12:21Z<p>David M. Rogers: </p>
<hr />
<div>{| cellpadding="4" style="border: 1px solid darkgray;"<br />
|- style="border: 1px solid darkgray;"<br />
|| Guy W. Dayhoff II and David M. Rogers, "Hydration and Dispersion Forces in Hydroxypropylcellulose Phase Behavior." [https://dx.doi.org/10.1021/acs.jpcb.9b01049 J. Phys. Chem B in press, 2019].<br />
<br />
We extend four forcefields to model hydroxypropylcellulose and find that none of them can reproduce experimentally measured hydration forces from 2001. Long-range solvent-mediated forces remain challenging targets for predictive simulation because of a breakdown in science funding priorities.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Range separation: The divide between local structures and field theories." [https://dx.doi.org/10.13128/Substantia-208 Substantia 3(1), 2019].<br />
<br />
This work presents parallel histories of the development of two modern theories of condensed matter: the theory of electron structure in quantum mechanics, and the theory of liquid structure in statistical mechanics. Key developments provide some guidance on important directions for future advancements in theory and practice.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Dual Characterization of the Ornstein-Zernike Equation in Moment Space." [https://arxiv.org/abs/1807.05963 submitted, 2019].<br />
<br />
I re-write Ornstein-Zernike theory in a convenient matrix basis so that future computational implementations can be made robust and that numerical and fitting error can be tightly controlled. It is hoped that the framework can be used in the near future to compute molecular solvation free energies and to realize its enormous potential economic and environmental benefits for formulating industrial fluids and consumer products.<br />
|- style="border: 1px solid darkgray;"<br />
|| Phillip S. Hudson, Stefan Boresch, David M. Rogers, and H. Lee Woodcock., "Accelerating QM/MM Free Energy Computations via Intramolecular Force Matching" [https://dx.doi.org/10.1021/acs.jctc.8b00517 J. Chem. Theory Comput., 14 (12):6327–35, 2018].<br />
<br />
My co-authors apply [https://github.com/frobnitzem/chemparam my algorithm and software implementation of Bayesian generalized linear model regression with linear inequality constraints] to estimate molecular modeling parameters from quantum their mechanical calculations. They find the method gives robust results that greatly increase efficiency of additional simulations.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Extension of Kirkwood-Buff theory to the canonical ensemble." [https://aip.scitation.org/doi/full/10.1063/1.5011696 J. Chem. Phys., 148:054102, 2018].<br />
<br />
We present a way to utilize Essmann et. al.'s smooth particle mesh Ewald algorithm ([https://github.com/frobnitzem/EwaldCorrel implemented here]) to get the low-angle direct correlation function from canonical ensemble simulation data. The result avoids well-documented issues with long wavelength (small-angle scattering) modes that appear when using real-space methods. This result is combined with new estimates of finite-size effects and grand-canonical ensemble corrections to provide definitive results on the problem of extrapolating Kirkwood-Buff integrals.<br />
|- style="border: 1px solid darkgray;"<br />
|| Juan M. Vanegas, Frank Heinrich, David M.Rogers, Bryan D. Carson, Sadie La Bauve, Briana C. Vernon, Bulent Akgun, Sushil Satija, Aihua Zheng, Margaret Kielian, Susan B. Rempe, and Michael S. Kent, "Insertion of Dengue E into lipid bilayers studied by neutron reflectivity and molecular dynamics simulations." [https://authors.elsevier.com/c/1WcOv1ClS9Jvp BBA 1860(5):1216-1230, 2018].<br />
<br />
We compare neutron reflectivity experiments to molecular dynamics calculations on the orientation and binding position<br />
of the Dengue envelope protein responsible for viral escape from the host cell's endosome. In addition to the hydrophobic fusion tip, we find important roles for three positively-charged residues in the viral protein that contribute to host membrane binding. These could potentially be targeted by new anti-viral medicines.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "An information theory model for dissipation in open quantum systems." [http://iopscience.iop.org/article/10.1088/1742-6596/880/1/012039 J. Phys., Conference Series 880(1):012039, 2017].<br />
<br />
This paper presents a new, simple ansatz for adding dissipation to arbitrary stochastic forcing of a quantum dynamical system.<br />
For Gaussian random forces, it predicts a Lindblad equation identical to the Caldeira-Leggett model <br />
up to order <math>\beta^2</math>, where the same term is present with a different prefactor.<br />
The system-centric, phase space picture here shows that the <math>\beta^2</math> term represents<br />
a quantum confinement effect.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Einstein-Podolsky-Rosen paradox implies a minimum achievable temperature." [http://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.012149 Phys. Rev. E 95, 012149, 2017.]<br />
<br />
This paper provides measurement-based definitions of heat and work that can be realized in current laboratory setups.<br />
The first and second laws are proved despite the fact that temperature is treated completely as as a property of the interacting reservoir. Measurements of the work are subject to the famous EPR paradox because the work exchanged between two quantum systems is not defined until a measurement is performed. Based on this, we show that even an environment at absolute zero cannot lower a system's temperature below a minimum characteristic of the way the environment is coupled to the system.<br />
|- style="border: 1px solid darkgray;"<br />
|| Guy W. Dayhoff II and David M. Rogers, "Driving forces in MD simulations of transition and ‘Free’ flows." [http://dx.doi.org/10.1080/08927022.2016.1273524 Mol. Sim. 43(5-6), pp. 467-477, 2017.] (special issue on Surface Chemistry)<br />
<br />
We set out to test the Joule-Thomson analysis of thermodynamics of porous flow for gasses through a nanopore and found that while local equilibrium is established in the steady-state, finite-size effects cause heat flow opposite the flow direction that violates the assumption of an adiabatic porous plug.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Efficient Primitives for Standard Tensor Linear Algebra." [https://doi.org/10.1145/2949550.2949580 Proc. XSEDE16 Conference on Diversity, Big Data, and Science at Scale, no. 14, 2016.]<br />
<br />
This paper introduces 3 basic functions that generalize BLAS to tensors and presents a code generation strategy for their [https://github.com/frobnitzem/slack efficient execution on GPUs] that achieves peak performance on the same order of magnitude as for traditional, vendor-optimized matrix-multiplications.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Overcoming the Minimum Image Constraint Using the Closest Point Search." [http://dx.doi.org/10.1016/j.jmgm.2016.07.004 J. Mol. Graph. Model 68, pp. 197–205, 2016.]<br />
<br />
An elegant solution to the problem of finding periodic images in non-rectangular lattices is provided based on the closest vector problem. Related code is here: [https://github.com/frobnitzem/pbctools]<br />
|- style="border: 1px solid darkgray;"<br />
|| Elisa La Bauve, Briana C. Vernon, Dongmei Ye, David M. Rogers, Cathryn M. Siegrist, Bryan Carson. Susan L. Rempe, Aihua Zheng, Margaret C. Kielian, Andrew P. Shreve, and Michael S. Kent. "Method for measuring the unbinding energy of strongly-bound membrane-associated proteins." [http://dx.doi.org/10.1016/j.bbamem.2016.07.004 BBA Biomembranes 1858(11): 2753–62, 2016.]<br />
<br />
This paper gives multiple experimental measurements of binding energy between the Dengue virus envelope protein<br />
and host membranes that largely confirm our computational predictions from 2015.<br />
I contributed all the theory for terminal velocity during sedimentation, along with a novel kinetic analysis providing the free energy and enthalpy of the dissociation barrier (all the details are at the end of the appendix).<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Thermodynamics of Maximum Transition Entropy for Quantum Assemblies." [http://arxiv.org/abs/1503.01232 arXiv:1503.01232 submitted, 2016].<br />
<br />
The work presents a new, general, theoretical foundation for the dynamics of open quantum systems modeled on the maximum entropy derivation of equilibrium statistical mechanics. Computational results are presented for three detailed systems to validate and reinforce the theory. It represents a significant advancement for the field, as it lucidly connects the dynamics of a single wavefunction plus environmental noise to the Caldeira-Leggett model for density matrices.<br />
|- style="border: 1px solid darkgray;"<br />
|| Andriy Anishkin, Juan M. Vanegas, David M. Rogers, Philip L. Lorenzi, Wai Kin Chan, Preeti Purwaha, John N. Weinstein, Sergei Sukharev, and Susan B. Rempe. "Catalytic Role of the Substrate Defines Specificity of Therapeutic L-Asparaginase."<br />
[http://dx.doi.org/10.1016/j.jmb.2015.06.017 J. Mol. Biol. 427:2867-2885, 2015].<br />
<br />
We present an explanation for the (until now controversial) catalytic mechanism of type 2 bacterial L-asparaginase enzymes.<br />
By using the carboxylic acid of the substrate (asparagine) as the proton acceptor, this enzyme is able to preferentially carry out deamidation on asparagine more quickly than for the competing substrate, glutamine. The hypothesis, re-discovered from our MD simulations, was first put forward years ago in contested experimental studies, and now finds additional support from our MD and QM calculations.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Towards a Direct, By-Need Evaluator for Dependently Typed Languages."<br />
[http://arxiv.org/abs/1509.07036 arXiv:1509.07036 submitted, 2015].<br />
<br />
This paper describes the implementation of a new interpreted language for distributed parallel computing.<br />
It achieves its goal by maintaining pure functional semantics,<br />
allowing all terms in the language to be partially evaluated and serialized to network storage<br />
at any point during computation.<br />
|- style="border: 1px solid darkgray;"<br />
|| Marielle Soniat, David M. Rogers, and Susan Rempe. "Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration." [http://pubs.acs.org/doi/abs/10.1021/acs.jctc.5b00357 J. Chem. Theory. Comput. 142:074101, 2015].<br />
<br />
We studied the influence of dispersion energy corrections on the free energy of formation for sodium-water clusters computed with DFT and wound up discovering that dispersion and split-range exchange functionals can somewhat counter-balance each other. The charged sodium ion pulls on the water's electrons, clearly showing which density functionals over-polarize compared to CCSD. Split-range exchange can reduce this over-polarization, but results in reduced electrostatic interaction. Dispersion can lower the binding energy again to counter-balance. So, functionals fit to experimental formation energies need both effects to avoid lowering energies by over-polarizing.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Real-space quadrature: a convenient, efficient representation for multipole expansions." [http://dx.doi.org/10.1063/1.4907404 J. Chem. Phys. 142:074101, 2015]. ([http://predictivestatmech.org/papers/real-poles.pdf Presentation])<br />
<br />
I introduce sets of point charges that are able to simultaneously reproduce all multipole (spherical harmonic) expansions up to arbitrary order. The number of points is space-optimal. Translations are described from the usual harmonics and from Cartesian moments (dipole, quadrupole, etc.) on supersymmetric tensors to directional moments using the point weight distribution. Many applications are possible, including trivial implementation of multipoles in molecular mechanics and representing probability distributions over rotation space.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Michael S. Kent, and Susan B. Rempe, "Molecular basis of endosomal-membrane association for the dengue virus envelope protein." [http://dx.doi.org/10.1016/j.bbamem.2014.12.018 BBA Biomembranes 1848(4):1041-52, 2015.]<br />
<br />
A fully atomistic potential of mean force for association of the viral envelope protein from Dengue virus was compared to a Poisson-Boltzmann electrostatic plus dispersion model. The results are consistent, showing hope for this type of combined scale simulation.<br />
|- style="border: 1px solid darkgray;"<br />
|| Yaqin Fu, Binsong Li, Ying-Bing Jiang, Darren R. Dunphy, Andy Tsai, Siu-Yue Tam, Hongyou Fan, Hongxia Zhan, David Rogers, Susan Rempe, Plamen Atanassov, Joseph L. Cecchi, and C. Jeffrey Brinker "Atomic Layer Deposition of L-Alanine Polypeptide." [http://pubs.acs.org/doi/abs/10.1021/ja5043403 JACS 136(45):15821–4, 2014.]<br />
<br />
This paper with our experimental collaborators carried out blocked peptide synthesis by vapor-depositing Boc-L-alanine to create a uniform thin film of polypeptides grown on a silica substrate activated by aminopropyltrimethoxysilane.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Silmaril, A Functional Language for Distributed Parallel Evaluation." [http://predictivestatmech.org/sil/papers/sil.pdf Submitted version]<br />
|- style="border: 1px solid darkgray;"<br />
|| Mathias B. Andersen, David M. Rogers, Junyu Mai, Benjamin Schudel, Anson V. Hatch, Susan B. Rempe and Ali Mani. "Spatiotemporal pH dynamics in concentration polarization near ion-selective membranes." [http://dx.doi.org/10.1021/la5014297 Langmuir, 30(26):7902–7912, 2014]<br />
|- style="border: 1px solid darkgray;"<br />
|| W. K. Chan, P. L. Lorenzi, A. Anishkin, P. Purwaha, D. M. Rogers, S. Sukharev, S.B. Rempe, and J. N. Weinstein. "The glutaminase activity of l-asparaginase is not required for anticancer activity against ASNS-negative cells." [http://dx.doi.org/10.1182/blood-2013-10-535112 Blood. 123(23):3596-606, 2014].<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Dian Jiao, Lawrence Pratt, and Susan B. Rempe. "Structural Models and Molecular Thermodynamics of Hydration of Ions and Small Molecules" [http://dx.doi.org/10.1016/B978-0-444-59440-2.00004-1 Annu. Rep. Comp. Chem. 8:71–127, 2012.]<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Susan B. Rempe. "Irreversible Thermodynamics." [http://dx.doi.org/10.1088/1742-6596/402/1/012014 J. Phys.: Conf. Ser. 402:012014, 2012].<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Thomas L. Beck, and Susan B. Rempe. [[Media:Dmroge_InfoNonequ2011.pdf|"An Information Theory Approach to Nonlinear, Nonequilibrium Thermodynamics."]] [http://dx.doi.org/10.1007/s10955-011-0358-9 J. Stat. Phys. 145(2):385-409, 2011]<br />
<br />
We show how the interpretation of thermodynamic states as representing system information leads naturally to thermodynamic cycles and the first and second laws of thermodynamics as well as similar formulations for nontrivial nonequilibrium problems. The logical development of the theory also leads naturally to correct indistinguishability factors in the partition function.<br />
|- style="border: 1px solid darkgray;"<br />
|| Sameer Varma, David M. Rogers, Lawrence R. Pratt, and Susan B. Rempe. "Perspectives on Ion Selectivity: Design Principles for K+ Selectivity in Membrane Transport." [http://jgp.rupress.org/content/137/6/479.full J. Gen. Physiol., 137(6):479-488, 2011.]<br />
<br />
We review the development of models for understanding the physical basis of selectivity for K+ ions over Na+, its sibling only one row behind, in membrane channels and transporters. Although the problem is subtle because of the morass of competing effects, we emphasize work analyzing the systematic influence of the environment on tipping local binding site structure toward selective configurations.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Susan B. Rempe. [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3443978/ “Probing the Thermodynamics of Competitive Ion Binding Using Minimum Energy Structures.”] [http://dx.doi.org/10.1021/jp2012864 J. Phys. Chem. B, 115(29):9116-29, 2011].<br />
<br />
We presented an extension of the Quasi-Chemical theory for quantifying the impact of local structure on ion complexation thermodynamics. The theory can be simply represented using a set of thermodynamic cycles involving binding site structural and compositional states as reaction intermediates.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| Susan B. Rempe and David M. Rogers; et. al. “Computational and experimental platform for understanding and optimizing water flux and salt rejection in nanoporous membranes.” [http://prod.sandia.gov/techlib/access-control.cgi/2010/106735.pdf Sandia Technical Report, SAND2010-6735, 2010.]<br />
<br />
We summarize work on designing polymer coatings for salt exclusion in water transporting nanopores. In this work, I collected available molecular dynamics results for these systems and performed a novel energy efficiency analysis able to relate atomistic and experimental scales as well as identify important design goals and chemical principles for material performance.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, [http://rave.ohiolink.edu/etdc/view?acc_num=ucin1251832030 ''''Using Bayes' Theorem for Free Energy Calculations''''], 2009.<br />
<br />
We investigated the central quantity of free energies in a Bayesian context and provide estimators for solvation free energies as well as optimal potential of mean force approximations to model polymer coarse-grained dynamics from atomistic simulations.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| Zhen Zhao, David M. Rogers and Thomas L. Beck. "Polarization and Charge Transfer in the Hydration of Chloride Ions." [http://link.aip.org/link/?JCP/132/014502/1 J. Chem. Phys., 132:014502, 2010.]<br />
<br />
Dr. Zhao's ab-initio analysis of the charge distribution in water-ion clusters highlighted the importance of many-body water-water interactions and charge transfer effects in determining cluster structural and energetic properties. These are still challenging to represent in modern polarizable forcefields and have implications for anion properties at interfaces.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Quasi-Chemical and Structural Analysis of Polarizable Anion Hydration." [http://link.aip.org/link/?JCP/132/014505/1 J. Chem. Phys., 132:014505, 2010.]<br />
<br />
The role of polarizability in forcefield-based models of ions and water was examined. Utilizing some of our recent developments on quasi-chemical theory, we have been able to quantify the tightened, asymmetric nature of the ion's local solvation waters induced by increased polarizability as well as the exact effects of polarization on the solvation free energy. The results suggest some potential problems and diagnostics for such models.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. [http://forcesolve.sourceforge.net/ Force Solve] (Sourceforge, Chicago IL, 2008).<br />
<br />
This force matching software implements and tests coarse-graining for general molecular systems in a mere 4000 lines of code. It is able to parametrize coarse Hamiltonians from atomic trajectory data given arbitrary definitions of coarse united-atom type models as well as carry out short Langevin Dynamics simulations on the coarse scale. The program's main drawbacks are its slow speed and high memory usage due to its simplistic design, attributable to the interpreted nature of python.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Resolution and Scale Independent Nonparametric Function Matching Using a String Energy Penalized Spline Prior." 2008. [http://arxiv.org/abs/1003.4741 arXiv:1003.4741v1] (stat.ML).<br />
<br />
Fresh insight is provided into long-standing mathematical issues surrounding computational modeling of continuous functions from a few sampled data points. The present research lays the groundwork for predicting the behavior of complicated many-body systems using advanced regression techniques.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Modeling molecular and ionic absolute solvation free energies with quasichemical theory bounds." [https://doi.org/10.1063/1.2985613 J. Chem. Phys., 129:134505, 2008.]<br />
<br />
We develop a Bayesian method for computing (with error bars) the free energy for forming a nano-bubble in an arbitrary solvent system. This forms the first step of a thermodynamic cycle for dissolving a real solute. We prove that upper and lower bounds for that solvation free energy can be obtained from two simulations (with and without the solute present). The method is excellent for dissolving gas in water, while the upper/lower bounds are larger for dissolving water or ions.<br />
|}<br />
<br />
== Manuscripts in Preparation/Submitted ==<br />
* [https://arxiv.org/abs/1712.09427 Fluctuation Theory of Ionic Solvation Potentials]<br />
* [https://arxiv.org/abs/1503.01232 Thermodynamics of Maximum Transition Entropy for Quantum Assemblies]<br />
* [https://arxiv.org/abs/1701.01466 Maximum Entropy Closure for Flows in Transiently Driven Nonequilibrium Systems]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=748Courses/PChemSpring20192019-04-16T22:31:51Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
** No Class Tuesday, Apr. 2<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
=== Mar. 19 ===<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
=== Mar. 28 ===<br />
<br />
[https://predictivestatmech.org/papers/group_wk.pdf Group Work Slides]<br />
<br />
Note: Assignment for Tuesday, Apr. 2 is on the last slide, above.<br />
It is due Thursday, Apr. 4!<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
# Part 4: (Ch. 5,6,9-10,13-14)<br />
#* Harmonic Oscillator: Ch. 5: 1-3, 7-10, 12-16, 18, 20-22, 27, 39-40<br />
#* Rigid Rotor: Ch. 5: 33-35, 37, 44-47<br />
#* Hydrogen Atom: Ch. 6: 4,5,8,13,20,27,29,32-36<br />
#* Other applications: Ch. 9:23, 24, 34, 36, 38; Ch. 10: 44-47<br />
#* Ch. 13: 1-5,7-9, Ch. 14: 2-5, 18-20<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# <u>For problem 2, choose one of the following two questions: (3 or 4, you do not have to do both)</u><br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
#* Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
# (<u> Problem 5 from class </u>) A Hadamard gate has matrix representation <math>H = \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]/\sqrt{2}</math>. A qbit initially in state <math>|0\rangle</math> is passed through the Hadamard gate to create an output state. Use <math>|0\rangle = \left[ \begin{array}{c}1 \\ 0\end{array}\right] </math> and <math>|1\rangle = \left[ \begin{array}{c}0 \\ 1\end{array}\right] </math> to compute each of the following:<br />
#* The probability of detecting the output state is equal to <math>|0\rangle</math><br />
#* The probability of detecting the output state is equal to <math>|1\rangle</math><br />
#* The expectation value of <math>X = 5 |0\rangle\langle 0| + 2 |1\rangle\langle 1|</math><br />
#* The expectation value <math>\langle 0|X H|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X H|0\rangle</math><br />
#* Which of the above corresponds to the expectation of the operator <math>X</math> when operating on the output state?<br />
<br />
{{note|Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
}}<br />
<br />
* Reference definitions and Bell state quantum circuit: [[File:definitions7.jpg|x100px]] [[File:BellIBM.png|x100px]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=747Courses/PChemSpring20192019-04-11T13:06:31Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
** No Class Tuesday, Apr. 2<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
=== Mar. 19 ===<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
=== Mar. 28 ===<br />
<br />
[https://predictivestatmech.org/papers/group_wk.pdf Group Work Slides]<br />
<br />
Note: Assignment for Tuesday, Apr. 2 is on the last slide, above.<br />
It is due Thursday, Apr. 4!<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
# Part 4: (Ch. 5,9-10,13-14)<br />
#* Harmonic Oscillator: 5: 1-3, 7-10, 12-16, 18, 20-22, 27, 39-40<br />
#* Rigid Rotor: 33-35, 37, 44-47<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# <u>For problem 2, choose one of the following two questions: (3 or 4, you do not have to do both)</u><br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
#* Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
# (<u> Problem 5 from class </u>) A Hadamard gate has matrix representation <math>H = \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]/\sqrt{2}</math>. A qbit initially in state <math>|0\rangle</math> is passed through the Hadamard gate to create an output state. Use <math>|0\rangle = \left[ \begin{array}{c}1 \\ 0\end{array}\right] </math> and <math>|1\rangle = \left[ \begin{array}{c}0 \\ 1\end{array}\right] </math> to compute each of the following:<br />
#* The probability of detecting the output state is equal to <math>|0\rangle</math><br />
#* The probability of detecting the output state is equal to <math>|1\rangle</math><br />
#* The expectation value of <math>X = 5 |0\rangle\langle 0| + 2 |1\rangle\langle 1|</math><br />
#* The expectation value <math>\langle 0|X H|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X H|0\rangle</math><br />
#* Which of the above corresponds to the expectation of the operator <math>X</math> when operating on the output state?<br />
<br />
{{note|Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
}}<br />
<br />
* Reference definitions and Bell state quantum circuit: [[File:definitions7.jpg|x100px]] [[File:BellIBM.png|x100px]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=746Courses/PChemSpring20192019-04-08T19:38:40Z<p>David M. Rogers: /* Special Assignment for Quiz 7 */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
** No Class Tuesday, Apr. 2<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
=== Mar. 19 ===<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
=== Mar. 28 ===<br />
<br />
[https://predictivestatmech.org/papers/group_wk.pdf Group Work Slides]<br />
<br />
Note: Assignment for Tuesday, Apr. 2 is on the last slide, above.<br />
It is due Thursday, Apr. 4!<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# <u>For problem 2, choose one of the following two questions: (3 or 4, you do not have to do both)</u><br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
#* Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
# (<u> Problem 5 from class </u>) A Hadamard gate has matrix representation <math>H = \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]/\sqrt{2}</math>. A qbit initially in state <math>|0\rangle</math> is passed through the Hadamard gate to create an output state. Use <math>|0\rangle = \left[ \begin{array}{c}1 \\ 0\end{array}\right] </math> and <math>|1\rangle = \left[ \begin{array}{c}0 \\ 1\end{array}\right] </math> to compute each of the following:<br />
#* The probability of detecting the output state is equal to <math>|0\rangle</math><br />
#* The probability of detecting the output state is equal to <math>|1\rangle</math><br />
#* The expectation value of <math>X = 5 |0\rangle\langle 0| + 2 |1\rangle\langle 1|</math><br />
#* The expectation value <math>\langle 0|X H|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X H|0\rangle</math><br />
#* Which of the above corresponds to the expectation of the operator <math>X</math> when operating on the output state?<br />
<br />
{{note|Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
}}<br />
<br />
* Reference definitions and Bell state quantum circuit: [[File:definitions7.jpg|x100px]] [[File:BellIBM.png|x100px]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=File:Definitions7.jpg&diff=745File:Definitions7.jpg2019-04-08T19:34:58Z<p>David M. Rogers: </p>
<hr />
<div></div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=744Courses/PChemSpring20192019-03-28T17:05:12Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
** No Class Tuesday, Apr. 2<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
=== Mar. 19 ===<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
=== Mar. 28 ===<br />
<br />
[https://predictivestatmech.org/papers/group_wk.pdf Group Work Slides]<br />
<br />
Note: Assignment for Tuesday, Apr. 2 is on the last slide, above.<br />
It is due Thursday, Apr. 4!<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# <u>For problem 2, choose one of the following two questions: (3 or 4, you do not have to do both)</u><br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
#* Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
# (<u> Problem 5 from class </u>) A Hadamard gate has matrix representation <math>H = \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]/\sqrt{2}</math>. A qbit initially in state <math>|0\rangle</math> is passed through the Hadamard gate to create an output state. Use <math>|0\rangle = \left[ \begin{array}{c}1 \\ 0\end{array}\right] </math> and <math>|1\rangle = \left[ \begin{array}{c}0 \\ 1\end{array}\right] </math> to compute each of the following:<br />
#* The probability of detecting the output state is equal to <math>|0\rangle</math><br />
#* The probability of detecting the output state is equal to <math>|1\rangle</math><br />
#* The expectation value of <math>X = 5 |0\rangle\langle 0| + 2 |1\rangle\langle 1|</math><br />
#* The expectation value <math>\langle 0|X H|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X H|0\rangle</math><br />
#* Which of the above corresponds to the expectation of the operator <math>X</math> when operating on the output state?<br />
<br />
{{note|Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
}}<br />
<br />
[[File:BellIBM.png|x100px]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=743Courses/PChemSpring20192019-03-28T17:00:49Z<p>David M. Rogers: /* Mar. 28 */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
=== Mar. 19 ===<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
=== Mar. 28 ===<br />
<br />
[https://predictivestatmech.org/papers/group_wk.pdf Group Work Slides]<br />
<br />
Note: Assignment for Tuesday, Apr. 2 is on the last slide, above.<br />
It is due Thursday, Apr. 4!<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# <u>For problem 2, choose one of the following two questions: (3 or 4, you do not have to do both)</u><br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
#* Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
# (<u> Problem 5 from class </u>) A Hadamard gate has matrix representation <math>H = \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]/\sqrt{2}</math>. A qbit initially in state <math>|0\rangle</math> is passed through the Hadamard gate to create an output state. Use <math>|0\rangle = \left[ \begin{array}{c}1 \\ 0\end{array}\right] </math> and <math>|1\rangle = \left[ \begin{array}{c}0 \\ 1\end{array}\right] </math> to compute each of the following:<br />
#* The probability of detecting the output state is equal to <math>|0\rangle</math><br />
#* The probability of detecting the output state is equal to <math>|1\rangle</math><br />
#* The expectation value of <math>X = 5 |0\rangle\langle 0| + 2 |1\rangle\langle 1|</math><br />
#* The expectation value <math>\langle 0|X H|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X H|0\rangle</math><br />
#* Which of the above corresponds to the expectation of the operator <math>X</math> when operating on the output state?<br />
<br />
{{note|Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
}}<br />
<br />
[[File:BellIBM.png|x100px]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=742Courses/PChemSpring20192019-03-28T17:00:32Z<p>David M. Rogers: /* Group Work */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
=== Mar. 19 ===<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
=== Mar. 28 ===<br />
<br />
[predictivestatmech.org/papers/group_wk.pdf Group Work Slides]<br />
<br />
Note: Assignment for Tuesday, Apr. 2 is on the last slide, above.<br />
It is due Thursday, Apr. 4!<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# <u>For problem 2, choose one of the following two questions: (3 or 4, you do not have to do both)</u><br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
#* Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
# (<u> Problem 5 from class </u>) A Hadamard gate has matrix representation <math>H = \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]/\sqrt{2}</math>. A qbit initially in state <math>|0\rangle</math> is passed through the Hadamard gate to create an output state. Use <math>|0\rangle = \left[ \begin{array}{c}1 \\ 0\end{array}\right] </math> and <math>|1\rangle = \left[ \begin{array}{c}0 \\ 1\end{array}\right] </math> to compute each of the following:<br />
#* The probability of detecting the output state is equal to <math>|0\rangle</math><br />
#* The probability of detecting the output state is equal to <math>|1\rangle</math><br />
#* The expectation value of <math>X = 5 |0\rangle\langle 0| + 2 |1\rangle\langle 1|</math><br />
#* The expectation value <math>\langle 0|X H|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X H|0\rangle</math><br />
#* Which of the above corresponds to the expectation of the operator <math>X</math> when operating on the output state?<br />
<br />
{{note|Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
}}<br />
<br />
[[File:BellIBM.png|x100px]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=741Courses/PChemSpring20192019-03-25T19:02:07Z<p>David M. Rogers: /* Special Assignment for Quiz 7 */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# <u>For problem 2, choose one of the following two questions: (3 or 4, you do not have to do both)</u><br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
#* Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
# (<u> Problem 5 from class </u>) A Hadamard gate has matrix representation <math>H = \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]/\sqrt{2}</math>. A qbit initially in state <math>|0\rangle</math> is passed through the Hadamard gate to create an output state. Use <math>|0\rangle = \left[ \begin{array}{c}1 \\ 0\end{array}\right] </math> and <math>|1\rangle = \left[ \begin{array}{c}0 \\ 1\end{array}\right] </math> to compute each of the following:<br />
#* The probability of detecting the output state is equal to <math>|0\rangle</math><br />
#* The probability of detecting the output state is equal to <math>|1\rangle</math><br />
#* The expectation value of <math>X = 5 |0\rangle\langle 0| + 2 |1\rangle\langle 1|</math><br />
#* The expectation value <math>\langle 0|X H|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X H|0\rangle</math><br />
#* Which of the above corresponds to the expectation of the operator <math>X</math> when operating on the output state?<br />
<br />
{{note|Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
}}<br />
<br />
[[File:BellIBM.png|x100px]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Template:Note&diff=740Template:Note2019-03-23T22:52:24Z<p>David M. Rogers: Created page with "<div style="background-color: #ddf5eb; border-style: dotted;"> {{{1}}} </div>"</p>
<hr />
<div><div style="background-color: #ddf5eb; border-style: dotted;"><br />
{{{1}}}<br />
</div></div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=739Courses/PChemSpring20192019-03-23T22:52:05Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# <u>For problem 2, choose one of the following two questions:</u><br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
#* Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
# (<u> Problem 5 from class </u>) A Hadamard gate has matrix representation <math>H = \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]/\sqrt{2}</math>. A qbit initially in state <math>|0\rangle</math> is passed through the Hadamard gate to create an output state. Use <math>|0\rangle = \left[ \begin{array}{c}1 \\ 0\end{array}\right] </math> and <math>|1\rangle = \left[ \begin{array}{c}0 \\ 1\end{array}\right] </math> to compute each of the following:<br />
#* The probability of detecting the output state is equal to <math>|0\rangle</math><br />
#* The probability of detecting the output state is equal to <math>|1\rangle</math><br />
#* The expectation value of <math>X = 5 |0\rangle\langle 0| + 2 |1\rangle\langle 1|</math><br />
#* The expectation value <math>\langle 0|X H|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X|0\rangle</math><br />
#* The expectation value <math>\langle 0|H X H|0\rangle</math><br />
#* Which of the above corresponds to the expectation of the operator <math>X</math> when operating on the output state?<br />
<br />
{{note|Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
}}<br />
<br />
[[File:BellIBM.png|x100px]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=738Courses/PChemSpring20192019-03-21T21:11:36Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
# Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
<br />
Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
<br />
[[File:BellIBM.png|x100px]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=File:BellIBM.png&diff=737File:BellIBM.png2019-03-21T21:10:43Z<p>David M. Rogers: Symmetric antiparallel Bell state created on IBM Q-experience.</p>
<hr />
<div>Symmetric antiparallel Bell state created on IBM Q-experience.</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=736Courses/PChemSpring20192019-03-21T20:46:27Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10<br />
<br />
=== Special Assignment for Quiz 7 ===<br />
<br />
# Provide, in your own words, definitions for each of the following: complete basis, expectation value, commutator, Hermitian operator, dimension, tunneling, nonlinear process, symmetry, continuous / continuity, integrable, divergent (of an expression), "existence" (of a math expression)<br />
# In the classical Bell experiment, a pair of 2 entangled particles are created in state <math>|\psi\rangle = (|0,1\rangle + |1,0\rangle)/\sqrt{2}</math>. A quantum circuit for creating such Bell states is given by the image below. Compute the final state of track (b) after each of the following measurements has occurred. Note that the two tracks are symmetric, so we can arbitrarily call the first quantum number ''track (a)'' and the second ''track (b)''. For hints, see the note on partial projection.<br />
#* Track (a) is measured and found to be in state <math>|0\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>|1\rangle</math>.<br />
#* Track (a) is measured and found to be in state <math>(|0\rangle+|1\rangle)/\sqrt{2}</math>.<br />
# Under the first scenario (track (a) is in state <math>|0\rangle</math>), what is the probability that track (b) can be measured in state <math>\cos(\theta)|0\rangle + \sin(\theta)|1\rangle</math>? Compare this to the Bell-state correlation function [https://en.wikipedia.org/wiki/Bell%27s_theorem].<br />
<br />
Partial projection is what happens to a quantum state when only one part of it is measured. The measured part must be projected into its known answer, while the rest of the state merely goes along for the ride. For our purposes, to do the partial projection of <math>|\psi\rangle</math> which results from finding that track (a) has state <math>|v\rangle</math>, compute <math>\langle v, ?| \psi \rangle</math> using <math>\langle v, ?| = (\langle v|)(\langle ?|)</math><br />
and use distributivity and orthogonality to get rid of all the track (a) state information. Factor off the <math>(\langle ?|)</math> and normalize the result to get the final state of track (b).<br />
<br />
[[File:BellIBM.jpg]]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=735Courses/PChemSpring20192019-03-19T19:37:15Z<p>David M. Rogers: /* Group Work */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
[[File:MeasProb1.jpg|x100px]]<br />
<br />
[[File:MeasProb2.jpg|x100px]]<br />
<br />
[[File:MeasProb3.jpg|x100px]]<br />
<br />
[[File:MeasProb5.jpg|x100px]]<br />
<br />
[[File:MeasProb4.jpg|x100px]]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=File:MeasProb5.jpg&diff=734File:MeasProb5.jpg2019-03-19T19:33:25Z<p>David M. Rogers: </p>
<hr />
<div></div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=File:MeasProb4.jpg&diff=733File:MeasProb4.jpg2019-03-19T19:32:52Z<p>David M. Rogers: </p>
<hr />
<div></div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=File:MeasProb3.jpg&diff=732File:MeasProb3.jpg2019-03-19T19:32:31Z<p>David M. Rogers: </p>
<hr />
<div></div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=File:MeasProb2.jpg&diff=731File:MeasProb2.jpg2019-03-19T19:32:07Z<p>David M. Rogers: </p>
<hr />
<div></div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=File:MeasProb1.jpg&diff=730File:MeasProb1.jpg2019-03-19T19:31:39Z<p>David M. Rogers: </p>
<hr />
<div></div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=729Courses/PChemSpring20192019-03-19T19:30:54Z<p>David M. Rogers: /* Group Work */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
[[File:MeasProb1.jpg]]<br />
<br />
[[File:MeasProb2.jpg]]<br />
<br />
[[File:MeasProb3.jpg]]<br />
<br />
[[File:MeasProb4.jpg]]<br />
<br />
[[File:MeasProb5.jpg]]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=728Courses/PChemSpring20192019-03-19T19:30:39Z<p>David M. Rogers: /* Group Work */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
[[File:MeasProb1.jpg]]<br />
[[File:MeasProb2.jpg]]<br />
[[File:MeasProb3.jpg]]<br />
[[File:MeasProb4.jpg]]<br />
[[File:MeasProb5.jpg]]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=727Courses/PChemSpring20192019-03-19T19:30:15Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Group Work ==<br />
<br />
[[File:MeasProb1.jpg]]<br />
<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=726Courses/PChemSpring20192019-03-18T22:54:10Z<p>David M. Rogers: /* Resources */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
** Sign up to [https://www.usf.edu/system/board-of-trustees/presidential-search-committee/meeting-schedule.aspx Attend an Executive Interview]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Publications&diff=725Publications2019-03-18T22:28:48Z<p>David M. Rogers: </p>
<hr />
<div>{| cellpadding="4" style="border: 1px solid darkgray;"<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Range separation: The divide between local structures and field theories." [https://arxiv.org/abs/1902.03289 in press, 2019].<br />
<br />
This work presents parallel histories of the development of two modern theories of condensed matter: the theory of electron structure in quantum mechanics, and the theory of liquid structure in statistical mechanics. Key developments provide some guidance on important directions for future advancements in theory and practice.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Dual Characterization of the Ornstein-Zernike Equation in Moment Space." [https://arxiv.org/abs/1807.05963 submitted, 2019].<br />
<br />
I re-write Ornstein-Zernike theory in a convenient matrix basis so that future computational implementations can be made robust and that numerical and fitting error can be tightly controlled. It is hoped that the framework can be used in the near future to compute molecular solvation free energies and to realize its enormous potential economic and environmental benefits for formulating industrial fluids and consumer products.<br />
|- style="border: 1px solid darkgray;"<br />
|| Phillip S. Hudson, Stefan Boresch, David M. Rogers, and H. Lee Woodcock., "Accelerating QM/MM Free Energy Computations via Intramolecular Force Matching" [https://dx.doi.org/10.1021/acs.jctc.8b00517 J. Chem. Theory Comput., 14 (12):6327–35, 2018].<br />
<br />
My co-authors apply [https://github.com/frobnitzem/chemparam my algorithm and software implementation of Bayesian generalized linear model regression with linear inequality constraints] to estimate molecular modeling parameters from quantum their mechanical calculations. They find the method gives robust results that greatly increase efficiency of additional simulations.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Extension of Kirkwood-Buff theory to the canonical ensemble." [https://aip.scitation.org/doi/full/10.1063/1.5011696 J. Chem. Phys., 148:054102, 2018].<br />
<br />
We present a way to utilize Essmann et. al.'s smooth particle mesh Ewald algorithm ([https://github.com/frobnitzem/EwaldCorrel implemented here]) to get the low-angle direct correlation function from canonical ensemble simulation data. The result avoids well-documented issues with long wavelength (small-angle scattering) modes that appear when using real-space methods. This result is combined with new estimates of finite-size effects and grand-canonical ensemble corrections to provide definitive results on the problem of extrapolating Kirkwood-Buff integrals.<br />
|- style="border: 1px solid darkgray;"<br />
|| Juan M. Vanegas, Frank Heinrich, David M.Rogers, Bryan D. Carson, Sadie La Bauve, Briana C. Vernon, Bulent Akgun, Sushil Satija, Aihua Zheng, Margaret Kielian, Susan B. Rempe, and Michael S. Kent, "Insertion of Dengue E into lipid bilayers studied by neutron reflectivity and molecular dynamics simulations." [https://authors.elsevier.com/c/1WcOv1ClS9Jvp BBA 1860(5):1216-1230, 2018].<br />
<br />
We compare neutron reflectivity experiments to molecular dynamics calculations on the orientation and binding position<br />
of the Dengue envelope protein responsible for viral escape from the host cell's endosome. In addition to the hydrophobic fusion tip, we find important roles for three positively-charged residues in the viral protein that contribute to host membrane binding. These could potentially be targeted by new anti-viral medicines.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "An information theory model for dissipation in open quantum systems." [http://iopscience.iop.org/article/10.1088/1742-6596/880/1/012039 J. Phys., Conference Series 880(1):012039, 2017].<br />
<br />
This paper presents a new, simple ansatz for adding dissipation to arbitrary stochastic forcing of a quantum dynamical system.<br />
For Gaussian random forces, it predicts a Lindblad equation identical to the Caldeira-Leggett model <br />
up to order <math>\beta^2</math>, where the same term is present with a different prefactor.<br />
The system-centric, phase space picture here shows that the <math>\beta^2</math> term represents<br />
a quantum confinement effect.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Einstein-Podolsky-Rosen paradox implies a minimum achievable temperature." [http://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.012149 Phys. Rev. E 95, 012149, 2017.]<br />
<br />
This paper provides measurement-based definitions of heat and work that can be realized in current laboratory setups.<br />
The first and second laws are proved despite the fact that temperature is treated completely as as a property of the interacting reservoir. Measurements of the work are subject to the famous EPR paradox because the work exchanged between two quantum systems is not defined until a measurement is performed. Based on this, we show that even an environment at absolute zero cannot lower a system's temperature below a minimum characteristic of the way the environment is coupled to the system.<br />
|- style="border: 1px solid darkgray;"<br />
|| Guy W. Dayhoff II and David M. Rogers, "Driving forces in MD simulations of transition and ‘Free’ flows." [http://dx.doi.org/10.1080/08927022.2016.1273524 Mol. Sim. 43(5-6), pp. 467-477, 2017.] (special issue on Surface Chemistry)<br />
<br />
We set out to test the Joule-Thomson analysis of thermodynamics of porous flow for gasses through a nanopore and found that while local equilibrium is established in the steady-state, finite-size effects cause heat flow opposite the flow direction that violates the assumption of an adiabatic porous plug.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Efficient Primitives for Standard Tensor Linear Algebra." [https://doi.org/10.1145/2949550.2949580 Proc. XSEDE16 Conference on Diversity, Big Data, and Science at Scale, no. 14, 2016.]<br />
<br />
This paper introduces 3 basic functions that generalize BLAS to tensors and presents a code generation strategy for their [https://github.com/frobnitzem/slack efficient execution on GPUs] that achieves peak performance on the same order of magnitude as for traditional, vendor-optimized matrix-multiplications.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Overcoming the Minimum Image Constraint Using the Closest Point Search." [http://dx.doi.org/10.1016/j.jmgm.2016.07.004 J. Mol. Graph. Model 68, pp. 197–205, 2016.]<br />
<br />
An elegant solution to the problem of finding periodic images in non-rectangular lattices is provided based on the closest vector problem. Related code is here: [https://github.com/frobnitzem/pbctools]<br />
|- style="border: 1px solid darkgray;"<br />
|| Elisa La Bauve, Briana C. Vernon, Dongmei Ye, David M. Rogers, Cathryn M. Siegrist, Bryan Carson. Susan L. Rempe, Aihua Zheng, Margaret C. Kielian, Andrew P. Shreve, and Michael S. Kent. "Method for measuring the unbinding energy of strongly-bound membrane-associated proteins." [http://dx.doi.org/10.1016/j.bbamem.2016.07.004 BBA Biomembranes 1858(11): 2753–62, 2016.]<br />
<br />
This paper gives multiple experimental measurements of binding energy between the Dengue virus envelope protein<br />
and host membranes that largely confirm our computational predictions from 2015.<br />
I contributed all the theory for terminal velocity during sedimentation, along with a novel kinetic analysis providing the free energy and enthalpy of the dissociation barrier (all the details are at the end of the appendix).<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Thermodynamics of Maximum Transition Entropy for Quantum Assemblies." [http://arxiv.org/abs/1503.01232 arXiv:1503.01232 submitted, 2016].<br />
<br />
The work presents a new, general, theoretical foundation for the dynamics of open quantum systems modeled on the maximum entropy derivation of equilibrium statistical mechanics. Computational results are presented for three detailed systems to validate and reinforce the theory. It represents a significant advancement for the field, as it lucidly connects the dynamics of a single wavefunction plus environmental noise to the Caldeira-Leggett model for density matrices.<br />
|- style="border: 1px solid darkgray;"<br />
|| Andriy Anishkin, Juan M. Vanegas, David M. Rogers, Philip L. Lorenzi, Wai Kin Chan, Preeti Purwaha, John N. Weinstein, Sergei Sukharev, and Susan B. Rempe. "Catalytic Role of the Substrate Defines Specificity of Therapeutic L-Asparaginase."<br />
[http://dx.doi.org/10.1016/j.jmb.2015.06.017 J. Mol. Biol. 427:2867-2885, 2015].<br />
<br />
We present an explanation for the (until now controversial) catalytic mechanism of type 2 bacterial L-asparaginase enzymes.<br />
By using the carboxylic acid of the substrate (asparagine) as the proton acceptor, this enzyme is able to preferentially carry out deamidation on asparagine more quickly than for the competing substrate, glutamine. The hypothesis, re-discovered from our MD simulations, was first put forward years ago in contested experimental studies, and now finds additional support from our MD and QM calculations.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Towards a Direct, By-Need Evaluator for Dependently Typed Languages."<br />
[http://arxiv.org/abs/1509.07036 arXiv:1509.07036 submitted, 2015].<br />
<br />
This paper describes the implementation of a new interpreted language for distributed parallel computing.<br />
It achieves its goal by maintaining pure functional semantics,<br />
allowing all terms in the language to be partially evaluated and serialized to network storage<br />
at any point during computation.<br />
|- style="border: 1px solid darkgray;"<br />
|| Marielle Soniat, David M. Rogers, and Susan Rempe. "Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration." [http://pubs.acs.org/doi/abs/10.1021/acs.jctc.5b00357 J. Chem. Theory. Comput. 142:074101, 2015].<br />
<br />
We studied the influence of dispersion energy corrections on the free energy of formation for sodium-water clusters computed with DFT and wound up discovering that dispersion and split-range exchange functionals can somewhat counter-balance each other. The charged sodium ion pulls on the water's electrons, clearly showing which density functionals over-polarize compared to CCSD. Split-range exchange can reduce this over-polarization, but results in reduced electrostatic interaction. Dispersion can lower the binding energy again to counter-balance. So, functionals fit to experimental formation energies need both effects to avoid lowering energies by over-polarizing.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Real-space quadrature: a convenient, efficient representation for multipole expansions." [http://dx.doi.org/10.1063/1.4907404 J. Chem. Phys. 142:074101, 2015]. ([http://predictivestatmech.org/papers/real-poles.pdf Presentation])<br />
<br />
I introduce sets of point charges that are able to simultaneously reproduce all multipole (spherical harmonic) expansions up to arbitrary order. The number of points is space-optimal. Translations are described from the usual harmonics and from Cartesian moments (dipole, quadrupole, etc.) on supersymmetric tensors to directional moments using the point weight distribution. Many applications are possible, including trivial implementation of multipoles in molecular mechanics and representing probability distributions over rotation space.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Michael S. Kent, and Susan B. Rempe, "Molecular basis of endosomal-membrane association for the dengue virus envelope protein." [http://dx.doi.org/10.1016/j.bbamem.2014.12.018 BBA Biomembranes 1848(4):1041-52, 2015.]<br />
<br />
A fully atomistic potential of mean force for association of the viral envelope protein from Dengue virus was compared to a Poisson-Boltzmann electrostatic plus dispersion model. The results are consistent, showing hope for this type of combined scale simulation.<br />
|- style="border: 1px solid darkgray;"<br />
|| Yaqin Fu, Binsong Li, Ying-Bing Jiang, Darren R. Dunphy, Andy Tsai, Siu-Yue Tam, Hongyou Fan, Hongxia Zhan, David Rogers, Susan Rempe, Plamen Atanassov, Joseph L. Cecchi, and C. Jeffrey Brinker "Atomic Layer Deposition of L-Alanine Polypeptide." [http://pubs.acs.org/doi/abs/10.1021/ja5043403 JACS 136(45):15821–4, 2014.]<br />
<br />
This paper with our experimental collaborators carried out blocked peptide synthesis by vapor-depositing Boc-L-alanine to create a uniform thin film of polypeptides grown on a silica substrate activated by aminopropyltrimethoxysilane.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Silmaril, A Functional Language for Distributed Parallel Evaluation." [http://predictivestatmech.org/sil/papers/sil.pdf Submitted version]<br />
|- style="border: 1px solid darkgray;"<br />
|| Mathias B. Andersen, David M. Rogers, Junyu Mai, Benjamin Schudel, Anson V. Hatch, Susan B. Rempe and Ali Mani. "Spatiotemporal pH dynamics in concentration polarization near ion-selective membranes." [http://dx.doi.org/10.1021/la5014297 Langmuir, 30(26):7902–7912, 2014]<br />
|- style="border: 1px solid darkgray;"<br />
|| W. K. Chan, P. L. Lorenzi, A. Anishkin, P. Purwaha, D. M. Rogers, S. Sukharev, S.B. Rempe, and J. N. Weinstein. "The glutaminase activity of l-asparaginase is not required for anticancer activity against ASNS-negative cells." [http://dx.doi.org/10.1182/blood-2013-10-535112 Blood. 123(23):3596-606, 2014].<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Dian Jiao, Lawrence Pratt, and Susan B. Rempe. "Structural Models and Molecular Thermodynamics of Hydration of Ions and Small Molecules" [http://dx.doi.org/10.1016/B978-0-444-59440-2.00004-1 Annu. Rep. Comp. Chem. 8:71–127, 2012.]<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Susan B. Rempe. "Irreversible Thermodynamics." [http://dx.doi.org/10.1088/1742-6596/402/1/012014 J. Phys.: Conf. Ser. 402:012014, 2012].<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Thomas L. Beck, and Susan B. Rempe. [[Media:Dmroge_InfoNonequ2011.pdf|"An Information Theory Approach to Nonlinear, Nonequilibrium Thermodynamics."]] [http://dx.doi.org/10.1007/s10955-011-0358-9 J. Stat. Phys. 145(2):385-409, 2011]<br />
<br />
We show how the interpretation of thermodynamic states as representing system information leads naturally to thermodynamic cycles and the first and second laws of thermodynamics as well as similar formulations for nontrivial nonequilibrium problems. The logical development of the theory also leads naturally to correct indistinguishability factors in the partition function.<br />
|- style="border: 1px solid darkgray;"<br />
|| Sameer Varma, David M. Rogers, Lawrence R. Pratt, and Susan B. Rempe. "Perspectives on Ion Selectivity: Design Principles for K+ Selectivity in Membrane Transport." [http://jgp.rupress.org/content/137/6/479.full J. Gen. Physiol., 137(6):479-488, 2011.]<br />
<br />
We review the development of models for understanding the physical basis of selectivity for K+ ions over Na+, its sibling only one row behind, in membrane channels and transporters. Although the problem is subtle because of the morass of competing effects, we emphasize work analyzing the systematic influence of the environment on tipping local binding site structure toward selective configurations.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Susan B. Rempe. [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3443978/ “Probing the Thermodynamics of Competitive Ion Binding Using Minimum Energy Structures.”] [http://dx.doi.org/10.1021/jp2012864 J. Phys. Chem. B, 115(29):9116-29, 2011].<br />
<br />
We presented an extension of the Quasi-Chemical theory for quantifying the impact of local structure on ion complexation thermodynamics. The theory can be simply represented using a set of thermodynamic cycles involving binding site structural and compositional states as reaction intermediates.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| Susan B. Rempe and David M. Rogers; et. al. “Computational and experimental platform for understanding and optimizing water flux and salt rejection in nanoporous membranes.” [http://prod.sandia.gov/techlib/access-control.cgi/2010/106735.pdf Sandia Technical Report, SAND2010-6735, 2010.]<br />
<br />
We summarize work on designing polymer coatings for salt exclusion in water transporting nanopores. In this work, I collected available molecular dynamics results for these systems and performed a novel energy efficiency analysis able to relate atomistic and experimental scales as well as identify important design goals and chemical principles for material performance.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, [http://rave.ohiolink.edu/etdc/view?acc_num=ucin1251832030 ''''Using Bayes' Theorem for Free Energy Calculations''''], 2009.<br />
<br />
We investigated the central quantity of free energies in a Bayesian context and provide estimators for solvation free energies as well as optimal potential of mean force approximations to model polymer coarse-grained dynamics from atomistic simulations.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| Zhen Zhao, David M. Rogers and Thomas L. Beck. "Polarization and Charge Transfer in the Hydration of Chloride Ions." [http://link.aip.org/link/?JCP/132/014502/1 J. Chem. Phys., 132:014502, 2010.]<br />
<br />
Dr. Zhao's ab-initio analysis of the charge distribution in water-ion clusters highlighted the importance of many-body water-water interactions and charge transfer effects in determining cluster structural and energetic properties. These are still challenging to represent in modern polarizable forcefields and have implications for anion properties at interfaces.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Quasi-Chemical and Structural Analysis of Polarizable Anion Hydration." [http://link.aip.org/link/?JCP/132/014505/1 J. Chem. Phys., 132:014505, 2010.]<br />
<br />
The role of polarizability in forcefield-based models of ions and water was examined. Utilizing some of our recent developments on quasi-chemical theory, we have been able to quantify the tightened, asymmetric nature of the ion's local solvation waters induced by increased polarizability as well as the exact effects of polarization on the solvation free energy. The results suggest some potential problems and diagnostics for such models.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. [http://forcesolve.sourceforge.net/ Force Solve] (Sourceforge, Chicago IL, 2008).<br />
<br />
This force matching software implements and tests coarse-graining for general molecular systems in a mere 4000 lines of code. It is able to parametrize coarse Hamiltonians from atomic trajectory data given arbitrary definitions of coarse united-atom type models as well as carry out short Langevin Dynamics simulations on the coarse scale. The program's main drawbacks are its slow speed and high memory usage due to its simplistic design, attributable to the interpreted nature of python.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Resolution and Scale Independent Nonparametric Function Matching Using a String Energy Penalized Spline Prior." 2008. [http://arxiv.org/abs/1003.4741 arXiv:1003.4741v1] (stat.ML).<br />
<br />
Fresh insight is provided into long-standing mathematical issues surrounding computational modeling of continuous functions from a few sampled data points. The present research lays the groundwork for predicting the behavior of complicated many-body systems using advanced regression techniques.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Modeling molecular and ionic absolute solvation free energies with quasichemical theory bounds." [https://doi.org/10.1063/1.2985613 J. Chem. Phys., 129:134505, 2008.]<br />
<br />
We develop a Bayesian method for computing (with error bars) the free energy for forming a nano-bubble in an arbitrary solvent system. This forms the first step of a thermodynamic cycle for dissolving a real solute. We prove that upper and lower bounds for that solvation free energy can be obtained from two simulations (with and without the solute present). The method is excellent for dissolving gas in water, while the upper/lower bounds are larger for dissolving water or ions.<br />
|}<br />
<br />
== Manuscripts in Preparation/Submitted ==<br />
* [https://arxiv.org/abs/1712.09427 Fluctuation Theory of Ionic Solvation Potentials]<br />
* [https://arxiv.org/abs/1503.01232 Thermodynamics of Maximum Transition Entropy for Quantum Assemblies]<br />
* [https://arxiv.org/abs/1701.01466 Maximum Entropy Closure for Flows in Transiently Driven Nonequilibrium Systems]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=724Courses/PChemSpring20192019-03-18T21:58:19Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
* [https://predictivestatmech.org/papers/LifeAfterGraduation.pdf Life After Graduation]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=723Courses/PChemSpring20192019-03-08T15:15:17Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
** [https://quantummechanics.ucsd.edu/ph130a/130_notes/130_notes.html Quantum Physics Online] (full year course)<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=722Courses/PChemSpring20192019-03-04T22:51:03Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
# Part 2: First Schrodinger Solutions (Ch. 3, C, E, F)<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
# Part 3: Measurement, Observables, Speakable and Unspeakable (Ch. 4-5)<br />
#* Ch. 4, 1-3, 5, 7, 11, 14-16, 21-22<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=721Courses/PChemSpring20192019-03-04T22:32:38Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://physicstoday.scitation.org/doi/10.1063/PT.3.2550 The Quantum Credo]<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
** [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
* Quantum Computing<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=720Courses/PChemSpring20192019-02-26T17:43:11Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
* [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
#* [[Media:HW6.pdf | Supplemental Homework for Quiz 6]]<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=File:HW6.pdf&diff=719File:HW6.pdf2019-02-26T17:41:44Z<p>David M. Rogers: </p>
<hr />
<div></div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=718Courses/PChemSpring20192019-02-25T22:08:54Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
** [https://quantumexperience.ng.bluemix.net/qx/experience Experiment with IBM's Quantum Computer]<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
* [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=717Courses/PChemSpring20192019-02-25T21:49:25Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
** [http://www.feynmanlectures.caltech.edu/III_09.html The Ammonia Maser]<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
* [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses&diff=716Courses2019-02-25T21:48:52Z<p>David M. Rogers: </p>
<hr />
<div>Here's a list of courses with useful online materials:<br />
<br />
== Courses ==<br />
* [[Courses/PChemSpring2019 | USF Physical Chemistry II (2019)]]<br />
* [[PChemFall2018| USF Physical Chemistry I (2018)]]<br />
* [[PChemFall2017| USF Physical Chemistry I (2017)]]<br />
* [[PChemFall2016| USF Physical Chemistry I (2016)]]<br />
* [[GradQuantumFall2013| USF Graduate Quantum Mechanics I]]<br />
* [[GradQuantumSpring2014| USF Graduate Quantum Mechanics II]]<br />
* [[CompSciSpring2018|Introduction to Scientific Computing (2018)]]<br />
* [[CompSciSpring2017|Introduction to Scientific Computing (2017)]]<br />
* [[CompSciSpring2016|Introduction to Scientific Computing (2016)]]<br />
* [[CompSciFall2014|Introduction to Scientific Computing (2014)]]<br />
* [http://lambda-the-ultimate.org/classic/Courses.html Functional Programming]<br />
<br />
== Lecture Series ==<br />
* [http://www.esqc.org/lectures European Summer School in Quantum Chemistry]<br />
<br />
== Tutorials ==<br />
* [[HowTo:Fourier|Fourier transforms]]<br />
* [http://www.mathematica-journal.com/2012/02/evaluation-of-gaussian-molecular-integrals Evaluating Matrix Elements]<br />
* [http://www.haskell.org/tutorial/ Haskell]<br />
* [http://monads.haskell.cz/html/index.html Monads]<br />
* [http://www.yosefk.com/blog/my-history-with-forth-stack-machines.html The Forth Language]<br />
<br />
== Reference Material ==<br />
* [http://dft.sandia.gov/Quest/DFT_codes.html List of DFT Codes]<br />
* [http://docs.python.org/3/tutorial/ Python Tutorial]<br />
* [http://www.nwchem-sw.org/index.php/Release62:NWChem_Documentation NWChem Documentation]<br />
* [http://www.ebi.ac.uk/pdbe-srv/pdbechem/ PDB Ligand Structures]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Publications&diff=715Publications2019-02-16T14:28:12Z<p>David M. Rogers: </p>
<hr />
<div>{| cellpadding="4" style="border: 1px solid darkgray;"<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Dual Characterization of the Ornstein-Zernike Equation in Moment Space." [https://arxiv.org/abs/1807.05963 submitted, 2019].<br />
<br />
I re-write Ornstein-Zernike theory in a convenient matrix basis so that future computational implementations can be made robust and that numerical and fitting error can be tightly controlled. It is hoped that the framework can be used in the near future to compute molecular solvation free energies and to realize its enormous potential economic and environmental benefits for formulating industrial fluids and consumer products.<br />
|- style="border: 1px solid darkgray;"<br />
|| Phillip S. Hudson, Stefan Boresch, David M. Rogers, and H. Lee Woodcock., "Accelerating QM/MM Free Energy Computations via Intramolecular Force Matching" [https://dx.doi.org/10.1021/acs.jctc.8b00517 J. Chem. Theory Comput., 14 (12):6327–35, 2018].<br />
<br />
My co-authors apply [https://github.com/frobnitzem/chemparam my algorithm and software implementation of Bayesian generalized linear model regression with linear inequality constraints] to estimate molecular modeling parameters from quantum their mechanical calculations. They find the method gives robust results that greatly increase efficiency of additional simulations.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Extension of Kirkwood-Buff theory to the canonical ensemble." [https://aip.scitation.org/doi/full/10.1063/1.5011696 J. Chem. Phys., 148:054102, 2018].<br />
<br />
We present a way to utilize Essmann et. al.'s smooth particle mesh Ewald algorithm ([https://github.com/frobnitzem/EwaldCorrel implemented here]) to get the low-angle direct correlation function from canonical ensemble simulation data. The result avoids well-documented issues with long wavelength (small-angle scattering) modes that appear when using real-space methods. This result is combined with new estimates of finite-size effects and grand-canonical ensemble corrections to provide definitive results on the problem of extrapolating Kirkwood-Buff integrals.<br />
|- style="border: 1px solid darkgray;"<br />
|| Juan M. Vanegas, Frank Heinrich, David M.Rogers, Bryan D. Carson, Sadie La Bauve, Briana C. Vernon, Bulent Akgun, Sushil Satija, Aihua Zheng, Margaret Kielian, Susan B. Rempe, and Michael S. Kent, "Insertion of Dengue E into lipid bilayers studied by neutron reflectivity and molecular dynamics simulations." [https://authors.elsevier.com/c/1WcOv1ClS9Jvp BBA 1860(5):1216-1230, 2018].<br />
<br />
We compare neutron reflectivity experiments to molecular dynamics calculations on the orientation and binding position<br />
of the Dengue envelope protein responsible for viral escape from the host cell's endosome. In addition to the hydrophobic fusion tip, we find important roles for three positively-charged residues in the viral protein that contribute to host membrane binding. These could potentially be targeted by new anti-viral medicines.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "An information theory model for dissipation in open quantum systems." [http://iopscience.iop.org/article/10.1088/1742-6596/880/1/012039 J. Phys., Conference Series 880(1):012039, 2017].<br />
<br />
This paper presents a new, simple ansatz for adding dissipation to arbitrary stochastic forcing of a quantum dynamical system.<br />
For Gaussian random forces, it predicts a Lindblad equation identical to the Caldeira-Leggett model <br />
up to order <math>\beta^2</math>, where the same term is present with a different prefactor.<br />
The system-centric, phase space picture here shows that the <math>\beta^2</math> term represents<br />
a quantum confinement effect.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Einstein-Podolsky-Rosen paradox implies a minimum achievable temperature." [http://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.012149 Phys. Rev. E 95, 012149, 2017.]<br />
<br />
This paper provides measurement-based definitions of heat and work that can be realized in current laboratory setups.<br />
The first and second laws are proved despite the fact that temperature is treated completely as as a property of the interacting reservoir. Measurements of the work are subject to the famous EPR paradox because the work exchanged between two quantum systems is not defined until a measurement is performed. Based on this, we show that even an environment at absolute zero cannot lower a system's temperature below a minimum characteristic of the way the environment is coupled to the system.<br />
|- style="border: 1px solid darkgray;"<br />
|| Guy W. Dayhoff II and David M. Rogers, "Driving forces in MD simulations of transition and ‘Free’ flows." [http://dx.doi.org/10.1080/08927022.2016.1273524 Mol. Sim. 43(5-6), pp. 467-477, 2017.] (special issue on Surface Chemistry)<br />
<br />
We set out to test the Joule-Thomson analysis of thermodynamics of porous flow for gasses through a nanopore and found that while local equilibrium is established in the steady-state, finite-size effects cause heat flow opposite the flow direction that violates the assumption of an adiabatic porous plug.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Efficient Primitives for Standard Tensor Linear Algebra." [https://doi.org/10.1145/2949550.2949580 Proc. XSEDE16 Conference on Diversity, Big Data, and Science at Scale, no. 14, 2016.]<br />
<br />
This paper introduces 3 basic functions that generalize BLAS to tensors and presents a code generation strategy for their [https://github.com/frobnitzem/slack efficient execution on GPUs] that achieves peak performance on the same order of magnitude as for traditional, vendor-optimized matrix-multiplications.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, "Overcoming the Minimum Image Constraint Using the Closest Point Search." [http://dx.doi.org/10.1016/j.jmgm.2016.07.004 J. Mol. Graph. Model 68, pp. 197–205, 2016.]<br />
<br />
An elegant solution to the problem of finding periodic images in non-rectangular lattices is provided based on the closest vector problem. Related code is here: [https://github.com/frobnitzem/pbctools]<br />
|- style="border: 1px solid darkgray;"<br />
|| Elisa La Bauve, Briana C. Vernon, Dongmei Ye, David M. Rogers, Cathryn M. Siegrist, Bryan Carson. Susan L. Rempe, Aihua Zheng, Margaret C. Kielian, Andrew P. Shreve, and Michael S. Kent. "Method for measuring the unbinding energy of strongly-bound membrane-associated proteins." [http://dx.doi.org/10.1016/j.bbamem.2016.07.004 BBA Biomembranes 1858(11): 2753–62, 2016.]<br />
<br />
This paper gives multiple experimental measurements of binding energy between the Dengue virus envelope protein<br />
and host membranes that largely confirm our computational predictions from 2015.<br />
I contributed all the theory for terminal velocity during sedimentation, along with a novel kinetic analysis providing the free energy and enthalpy of the dissociation barrier (all the details are at the end of the appendix).<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Thermodynamics of Maximum Transition Entropy for Quantum Assemblies." [http://arxiv.org/abs/1503.01232 arXiv:1503.01232 submitted, 2016].<br />
<br />
The work presents a new, general, theoretical foundation for the dynamics of open quantum systems modeled on the maximum entropy derivation of equilibrium statistical mechanics. Computational results are presented for three detailed systems to validate and reinforce the theory. It represents a significant advancement for the field, as it lucidly connects the dynamics of a single wavefunction plus environmental noise to the Caldeira-Leggett model for density matrices.<br />
|- style="border: 1px solid darkgray;"<br />
|| Andriy Anishkin, Juan M. Vanegas, David M. Rogers, Philip L. Lorenzi, Wai Kin Chan, Preeti Purwaha, John N. Weinstein, Sergei Sukharev, and Susan B. Rempe. "Catalytic Role of the Substrate Defines Specificity of Therapeutic L-Asparaginase."<br />
[http://dx.doi.org/10.1016/j.jmb.2015.06.017 J. Mol. Biol. 427:2867-2885, 2015].<br />
<br />
We present an explanation for the (until now controversial) catalytic mechanism of type 2 bacterial L-asparaginase enzymes.<br />
By using the carboxylic acid of the substrate (asparagine) as the proton acceptor, this enzyme is able to preferentially carry out deamidation on asparagine more quickly than for the competing substrate, glutamine. The hypothesis, re-discovered from our MD simulations, was first put forward years ago in contested experimental studies, and now finds additional support from our MD and QM calculations.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Towards a Direct, By-Need Evaluator for Dependently Typed Languages."<br />
[http://arxiv.org/abs/1509.07036 arXiv:1509.07036 submitted, 2015].<br />
<br />
This paper describes the implementation of a new interpreted language for distributed parallel computing.<br />
It achieves its goal by maintaining pure functional semantics,<br />
allowing all terms in the language to be partially evaluated and serialized to network storage<br />
at any point during computation.<br />
|- style="border: 1px solid darkgray;"<br />
|| Marielle Soniat, David M. Rogers, and Susan Rempe. "Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration." [http://pubs.acs.org/doi/abs/10.1021/acs.jctc.5b00357 J. Chem. Theory. Comput. 142:074101, 2015].<br />
<br />
We studied the influence of dispersion energy corrections on the free energy of formation for sodium-water clusters computed with DFT and wound up discovering that dispersion and split-range exchange functionals can somewhat counter-balance each other. The charged sodium ion pulls on the water's electrons, clearly showing which density functionals over-polarize compared to CCSD. Split-range exchange can reduce this over-polarization, but results in reduced electrostatic interaction. Dispersion can lower the binding energy again to counter-balance. So, functionals fit to experimental formation energies need both effects to avoid lowering energies by over-polarizing.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Real-space quadrature: a convenient, efficient representation for multipole expansions." [http://dx.doi.org/10.1063/1.4907404 J. Chem. Phys. 142:074101, 2015]. ([http://predictivestatmech.org/papers/real-poles.pdf Presentation])<br />
<br />
I introduce sets of point charges that are able to simultaneously reproduce all multipole (spherical harmonic) expansions up to arbitrary order. The number of points is space-optimal. Translations are described from the usual harmonics and from Cartesian moments (dipole, quadrupole, etc.) on supersymmetric tensors to directional moments using the point weight distribution. Many applications are possible, including trivial implementation of multipoles in molecular mechanics and representing probability distributions over rotation space.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Michael S. Kent, and Susan B. Rempe, "Molecular basis of endosomal-membrane association for the dengue virus envelope protein." [http://dx.doi.org/10.1016/j.bbamem.2014.12.018 BBA Biomembranes 1848(4):1041-52, 2015.]<br />
<br />
A fully atomistic potential of mean force for association of the viral envelope protein from Dengue virus was compared to a Poisson-Boltzmann electrostatic plus dispersion model. The results are consistent, showing hope for this type of combined scale simulation.<br />
|- style="border: 1px solid darkgray;"<br />
|| Yaqin Fu, Binsong Li, Ying-Bing Jiang, Darren R. Dunphy, Andy Tsai, Siu-Yue Tam, Hongyou Fan, Hongxia Zhan, David Rogers, Susan Rempe, Plamen Atanassov, Joseph L. Cecchi, and C. Jeffrey Brinker "Atomic Layer Deposition of L-Alanine Polypeptide." [http://pubs.acs.org/doi/abs/10.1021/ja5043403 JACS 136(45):15821–4, 2014.]<br />
<br />
This paper with our experimental collaborators carried out blocked peptide synthesis by vapor-depositing Boc-L-alanine to create a uniform thin film of polypeptides grown on a silica substrate activated by aminopropyltrimethoxysilane.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers. "Silmaril, A Functional Language for Distributed Parallel Evaluation." [http://predictivestatmech.org/sil/papers/sil.pdf Submitted version]<br />
|- style="border: 1px solid darkgray;"<br />
|| Mathias B. Andersen, David M. Rogers, Junyu Mai, Benjamin Schudel, Anson V. Hatch, Susan B. Rempe and Ali Mani. "Spatiotemporal pH dynamics in concentration polarization near ion-selective membranes." [http://dx.doi.org/10.1021/la5014297 Langmuir, 30(26):7902–7912, 2014]<br />
|- style="border: 1px solid darkgray;"<br />
|| W. K. Chan, P. L. Lorenzi, A. Anishkin, P. Purwaha, D. M. Rogers, S. Sukharev, S.B. Rempe, and J. N. Weinstein. "The glutaminase activity of l-asparaginase is not required for anticancer activity against ASNS-negative cells." [http://dx.doi.org/10.1182/blood-2013-10-535112 Blood. 123(23):3596-606, 2014].<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Dian Jiao, Lawrence Pratt, and Susan B. Rempe. "Structural Models and Molecular Thermodynamics of Hydration of Ions and Small Molecules" [http://dx.doi.org/10.1016/B978-0-444-59440-2.00004-1 Annu. Rep. Comp. Chem. 8:71–127, 2012.]<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Susan B. Rempe. "Irreversible Thermodynamics." [http://dx.doi.org/10.1088/1742-6596/402/1/012014 J. Phys.: Conf. Ser. 402:012014, 2012].<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, Thomas L. Beck, and Susan B. Rempe. [[Media:Dmroge_InfoNonequ2011.pdf|"An Information Theory Approach to Nonlinear, Nonequilibrium Thermodynamics."]] [http://dx.doi.org/10.1007/s10955-011-0358-9 J. Stat. Phys. 145(2):385-409, 2011]<br />
<br />
We show how the interpretation of thermodynamic states as representing system information leads naturally to thermodynamic cycles and the first and second laws of thermodynamics as well as similar formulations for nontrivial nonequilibrium problems. The logical development of the theory also leads naturally to correct indistinguishability factors in the partition function.<br />
|- style="border: 1px solid darkgray;"<br />
|| Sameer Varma, David M. Rogers, Lawrence R. Pratt, and Susan B. Rempe. "Perspectives on Ion Selectivity: Design Principles for K+ Selectivity in Membrane Transport." [http://jgp.rupress.org/content/137/6/479.full J. Gen. Physiol., 137(6):479-488, 2011.]<br />
<br />
We review the development of models for understanding the physical basis of selectivity for K+ ions over Na+, its sibling only one row behind, in membrane channels and transporters. Although the problem is subtle because of the morass of competing effects, we emphasize work analyzing the systematic influence of the environment on tipping local binding site structure toward selective configurations.<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Susan B. Rempe. [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3443978/ “Probing the Thermodynamics of Competitive Ion Binding Using Minimum Energy Structures.”] [http://dx.doi.org/10.1021/jp2012864 J. Phys. Chem. B, 115(29):9116-29, 2011].<br />
<br />
We presented an extension of the Quasi-Chemical theory for quantifying the impact of local structure on ion complexation thermodynamics. The theory can be simply represented using a set of thermodynamic cycles involving binding site structural and compositional states as reaction intermediates.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| Susan B. Rempe and David M. Rogers; et. al. “Computational and experimental platform for understanding and optimizing water flux and salt rejection in nanoporous membranes.” [http://prod.sandia.gov/techlib/access-control.cgi/2010/106735.pdf Sandia Technical Report, SAND2010-6735, 2010.]<br />
<br />
We summarize work on designing polymer coatings for salt exclusion in water transporting nanopores. In this work, I collected available molecular dynamics results for these systems and performed a novel energy efficiency analysis able to relate atomistic and experimental scales as well as identify important design goals and chemical principles for material performance.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers, [http://rave.ohiolink.edu/etdc/view?acc_num=ucin1251832030 ''''Using Bayes' Theorem for Free Energy Calculations''''], 2009.<br />
<br />
We investigated the central quantity of free energies in a Bayesian context and provide estimators for solvation free energies as well as optimal potential of mean force approximations to model polymer coarse-grained dynamics from atomistic simulations.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| Zhen Zhao, David M. Rogers and Thomas L. Beck. "Polarization and Charge Transfer in the Hydration of Chloride Ions." [http://link.aip.org/link/?JCP/132/014502/1 J. Chem. Phys., 132:014502, 2010.]<br />
<br />
Dr. Zhao's ab-initio analysis of the charge distribution in water-ion clusters highlighted the importance of many-body water-water interactions and charge transfer effects in determining cluster structural and energetic properties. These are still challenging to represent in modern polarizable forcefields and have implications for anion properties at interfaces.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Quasi-Chemical and Structural Analysis of Polarizable Anion Hydration." [http://link.aip.org/link/?JCP/132/014505/1 J. Chem. Phys., 132:014505, 2010.]<br />
<br />
The role of polarizability in forcefield-based models of ions and water was examined. Utilizing some of our recent developments on quasi-chemical theory, we have been able to quantify the tightened, asymmetric nature of the ion's local solvation waters induced by increased polarizability as well as the exact effects of polarization on the solvation free energy. The results suggest some potential problems and diagnostics for such models.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. [http://forcesolve.sourceforge.net/ Force Solve] (Sourceforge, Chicago IL, 2008).<br />
<br />
This force matching software implements and tests coarse-graining for general molecular systems in a mere 4000 lines of code. It is able to parametrize coarse Hamiltonians from atomic trajectory data given arbitrary definitions of coarse united-atom type models as well as carry out short Langevin Dynamics simulations on the coarse scale. The program's main drawbacks are its slow speed and high memory usage due to its simplistic design, attributable to the interpreted nature of python.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Resolution and Scale Independent Nonparametric Function Matching Using a String Energy Penalized Spline Prior." 2008. [http://arxiv.org/abs/1003.4741 arXiv:1003.4741v1] (stat.ML).<br />
<br />
Fresh insight is provided into long-standing mathematical issues surrounding computational modeling of continuous functions from a few sampled data points. The present research lays the groundwork for predicting the behavior of complicated many-body systems using advanced regression techniques.<br />
<br />
|- style="border: 1px solid darkgray;"<br />
|| David M. Rogers and Thomas L. Beck. "Modeling molecular and ionic absolute solvation free energies with quasichemical theory bounds." [https://doi.org/10.1063/1.2985613 J. Chem. Phys., 129:134505, 2008.]<br />
<br />
We develop a Bayesian method for computing (with error bars) the free energy for forming a nano-bubble in an arbitrary solvent system. This forms the first step of a thermodynamic cycle for dissolving a real solute. We prove that upper and lower bounds for that solvation free energy can be obtained from two simulations (with and without the solute present). The method is excellent for dissolving gas in water, while the upper/lower bounds are larger for dissolving water or ions.<br />
|}<br />
<br />
== Manuscripts in Preparation/Submitted ==<br />
* [https://arxiv.org/abs/1712.09427 Fluctuation Theory of Ionic Solvation Potentials]<br />
* [https://arxiv.org/abs/1503.01232 Thermodynamics of Maximum Transition Entropy for Quantum Assemblies]<br />
* [https://arxiv.org/abs/1701.01466 Maximum Entropy Closure for Flows in Transiently Driven Nonequilibrium Systems]</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=714Courses/PChemSpring20192019-02-15T19:49:13Z<p>David M. Rogers: /* Assigned Homework Problems */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
* [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.<br />
<br />
=== Special Assignment for Quiz 4 ===<br />
<br />
{| class="wikitable"<br />
|-<br />
| <math> f_1(x) = e^{ikx} </math><br />
| <math> f_2(x) = 2 i e^{-2x} </math><br />
| <math> f_3(x) = 7 x </math><br />
| <math> f_4(x) = x^2 - 1 </math><br />
| <math> f_5(x) = sin(2 \pi x/a) </math><br />
|}<br />
<br />
# For each of the following operators, list all of the functions above which are eigenfunctions. There may be more than one. For each, also identify the corresponding eigenvalue.<br />
#* <math>\hat P = -i\hbar \frac{d}{dx}</math><br />
#* <math>\hat S = 3</math><br />
#* <math>\hat R = 2 x \frac{d}{dx} - 1</math><br />
#* <math>\hat H = -c \frac{d^2}{dx^2} </math><br />
# Find the normalization constant needed for each of the functions, <math>f_1 -- f_5</math> so that <math>\int_0^a (A_n f_n(x))^2 = 1</math><br />
#* <math>A_1 = </math><br />
#* <math>A_2 = </math><br />
#* <math>A_3 = </math><br />
#* <math>A_4 = </math> <br />
#* <math>A_5 = </math><br />
# Complete the following problems from the text:<br />
#* 3-1<br />
#* 3-3<br />
#* 3-4<br />
#* 3-5<br />
#* 3-10</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=713Courses/PChemSpring20192019-02-12T16:12:24Z<p>David M. Rogers: /* Assigned Homework Problems */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
* [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=712Courses/PChemSpring20192019-02-12T16:04:21Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
* [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b\x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35<br />
#* Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11<br />
#** We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=711Courses/PChemSpring20192019-01-31T21:10:52Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
<br />
* Quantum Advances Nobel Prize Lectures<br />
** [https://www.nobelprize.org/prizes/chemistry/2013/karplus/facts/ Karplus, Levitt and Warshel, 2013]<br />
** [https://www.nobelprize.org/prizes/physics/2012/haroche/facts/ Haroche and Wineland, 2012]<br />
** [https://www.nobelprize.org/prizes/physics/2005/hall/facts/ Glauber, Hall, and Hänsch, 2005]<br />
** [https://www.nobelprize.org/prizes/chemistry/1998/kohn/facts/ Kohn and Pople, 1998]<br />
** [https://www.nobelprize.org/prizes/chemistry/1992/marcus/facts/ Rudolph Marcus, 1992]<br />
** [https://www.nobelprize.org/prizes/chemistry/1991/ernst/facts/ Richard Ernst, 1991]<br />
** [https://www.nobelprize.org/prizes/physics/1954/born/facts/ Born and Bothe, 1954]<br />
** [https://www.nobelprize.org/prizes/physics/1952/bloch/biographical/ Bloch and Purcell, 1952]<br />
** [https://www.nobelprize.org/prizes/physics/1945/pauli/facts/ Wolfgang Pauli, 1945]<br />
** [https://www.nobelprize.org/prizes/physics/1933/schrodinger/facts/ Schrödinger and Dirac, 1933]<br />
** [https://www.nobelprize.org/prizes/physics/1932/heisenberg/facts/ Werner Heisenberg, 1932]<br />
** [https://www.nobelprize.org/prizes/physics/1921/einstein/facts/ Albert Einstein, 1921]<br />
** [https://www.nobelprize.org/prizes/physics/1918/planck/facts/ Max Planck, 1918]<br />
<br />
* Advanced reading:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons] (Haroche and Raimond's book)<br />
<br />
* Super-advanced reading:<br />
** [https://doi.org/10.1017/9781316995457 Collapse of The Wave Function]<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
* [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b\x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=710Courses/PChemSpring20192019-01-31T20:36:01Z<p>David M. Rogers: </p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
* Optional Extras:<br />
** [https://dx.doi.org/10.1093/acprof:oso/9780198509141.001.0001 Exploring the Quantum: Atoms, Cavities, and Photons]<br />
** [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
** [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
* [https://www.youtube.com/watch?v=RXPlHa5mRBE Audio in general]<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b\x) and check<br />
#** Hint on 5: use exp(i omega t) = ...<br />
#* Ch. 3, 1-19,24,25,28,29,30,32,35</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=709Courses/PChemSpring20192019-01-14T20:07:03Z<p>David M. Rogers: /* Resources */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
* [http://www.feynmanlectures.caltech.edu/I_22.html Complex Algebra]<br />
* [http://www.feynmanlectures.caltech.edu/I_23.html Damped, Driven Harmonic Oscillator]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b\x) and check<br />
#** Hint on 5: use exp(i omega t) = ...</div>David M. Rogershttps://www.predictivestatmech.org/w/index.php?title=Courses/PChemSpring2019&diff=708Courses/PChemSpring20192019-01-14T20:06:02Z<p>David M. Rogers: /* Resources */</p>
<hr />
<div>'''<BIG>Physical Chemistry II</BIG>'''<br />
<br />
Course Info<br />
* Course Numbers CHM 4411-001<br />
* Credit Hours: 4<br />
* Meeting Dates: Jan. 8 - Apr. 23, 2019<br />
** No Class Mar. 11-17<br />
* Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048<br />
** Problem Sessions: Fri., 11am-12 pm in ISA 3050<br />
** Regular quizzes on Fridays<br />
** Office Hours: Fri., 10-11 am in IDR 200<br />
<br />
* Grading:<br />
** Quiz (30%)<br />
*** To succeed in the quiz, complete the homework and study the topics covered in the previous week!<br />
** Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)<br />
** Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)<br />
** Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)<br />
<br />
== Overview and Objectives ==<br />
<br />
This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.<br />
<br />
Students in this course will demonstrate the ability to apply the following ideas:<br />
<br />
* Relationship between mathematical models and intermolecular forces.<br />
* Explaining quantum states and their mathematical and physical properties.<br />
* Connecting observed molecular properties with quantum measurements.<br />
* Calculation of quantum energy levels and spectra.<br />
<br />
== Textbooks ==<br />
<br />
* McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.<br />
<br />
== Resources ==<br />
<br />
* Visualization of Modes:<br />
** [https://www.youtube.com/watch?v=BE827gwnnk4 Wine Glass]<br />
** [https://www.youtube.com/watch?v=v4ELxKKT5Rw&t=4s Drum Head] [https://youtu.be/QksHbCwYngw?t=5 see also]<br />
*** Note: Modes are indexed by 2 numbers for a 2D surface.<br />
** [https://www.youtube.com/watch?v=Qf0t4qIVWF4 Another 2D example]<br />
*** This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.<br />
** [https://www.youtube.com/watch?v=6JeyiM0YNo4 Violin String]<br />
*** Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.<br />
** [https://youtu.be/0Ddr_ipAMqE?t=224 Cymbals]<br />
*** Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.<br />
** [https://www.youtube.com/watch?v=fMsjyQHtmiU Tacoma Narrows Bridge]<br />
*** Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.<br />
<br />
* Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math><br />
** Here is Henri Poincaré's [https://www.gutenberg.org/files/37157/37157-pdf.pdf Science and Hypothesis], 1905. <blockquote><br />
[On finding atomic causes of laboratory observations,] I shall only give one example which has always struck me rather forcibly. If I decompose white light, I shall be able to isolate a portion of the spectrum, but however small it may be, it will always be a certain width. In the same way the natural lights which are called monochromatic give us a very fine ray, but one which is not, however, infinitely fine. It might be supposed that in the experimental study of the properties of these natural lights, by operating with finer and finer rays, and passing on at last to the limit, so to speak, we should eventually obtain the properties of a rigorously monochromatic light. That would not be accurate. I assume that two rays emanate from the same source, that they are first polarised in planes at right angles, that they are then brought back again to the same plane<br />
of polarisation, and that we try to obtain interference. If the light were rigorously monochromatic, there would be interference; but with our nearly monochromatic lights, there will be no interference, and that, however narrow the ray may be. For it to be otherwise, the ray would have to be several million times finer than the finest known rays.<br />
</blockquote><br />
** He is saying that sunlight and light from incandescent bulbs has a continuous spectrum of all frequencies. Light from atomic transitions (like a high-pressure sodium lamp) has discrete spectral lines, but those ''still'' have a tiny line-width and two independent polarizations. This was not understood before the fundamental dogma of spectroscopy. The line-width is due to the energy-time uncertainty principle.<br />
<br />
* [Complex Algebra http://www.feynmanlectures.caltech.edu/I_22.html]<br />
* [Harmonic Resonance Phenomena http://www.feynmanlectures.caltech.edu/I_23.html]<br />
<br />
== Assigned Homework Problems ==<br />
<br />
# Part 1: Origins (Ch. 1, A, and 2)<br />
#* Ch. 1, 1-40 (we'll do 41-44 in class)<br />
#* Ch. A, 1-14<br />
#** Hint on 12: use i = exp(...)<br />
#* Ch. 2, 1-16, 19<br />
#** Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b\x) and check<br />
#** Hint on 5: use exp(i omega t) = ...</div>David M. Rogers