# Courses/PChemSpring2019

**Physical Chemistry II**

Course Info

- Course Numbers CHM 4411-001
- Credit Hours: 4
- Meeting Dates: Jan. 8 - Apr. 23, 2019
- No Class Mar. 11-17

- Meeting Times: Tues. and Thurs., 9:30-10:45 am in ISA 3048
- Problem Sessions: Fri., 11am-12 pm in ISA 3050
- Regular quizzes on Fridays
- Office Hours: Fri., 10-11 am in IDR 200

- Grading:
- Quiz (30%)
- To succeed in the quiz, complete the homework and study the topics covered in the previous week!

- Exam 1 (20%) Fri., Feb. 8 11am-12pm (ISA 3050)
- Exam 2 (20%) Fri., Mar. 8, 11am-12pm (ISA 3050)
- Final (30%) Thurs., May 2 7:30-9:30am (ISA 3048)

- Quiz (30%)

## Contents

## Overview and Objectives

This course will introduce you to quantum theory, important for quantitatively describing atomic and molecular structure, chemical bonding and spectra.

Students in this course will demonstrate the ability to apply the following ideas:

- Relationship between mathematical models and intermolecular forces.
- Explaining quantum states and their mathematical and physical properties.
- Connecting observed molecular properties with quantum measurements.
- Calculation of quantum energy levels and spectra.

## Textbooks

- McQuarrie and Simon, Physical Chemistry: A Molecular Approach, University Science Books, 1997. ISBN: 0935702997.
- Optional Extras:

- Quantum Advances Nobel Prize Lectures
- Karplus, Levitt and Warshel, 2013
- Haroche and Wineland, 2012
- Glauber, Hall, and Hänsch, 2005
- Kohn and Pople, 1998
- Rudolph Marcus, 1992
- Richard Ernst, 1991
- Born and Bothe, 1954
- Bloch and Purcell, 1952
- Wolfgang Pauli, 1945
- Schrödinger and Dirac, 1933
- Werner Heisenberg, 1932
- Albert Einstein, 1921
- Max Planck, 1918

- Advanced reading:
- Exploring the Quantum: Atoms, Cavities, and Photons (Haroche and Raimond's book)

- Super-advanced reading:

## Resources

- Visualization of Modes:
- Wine Glass
- Drum Head see also
- Note: Modes are indexed by 2 numbers for a 2D surface.

- Another 2D example
- This one is part-way between a particle in a 2D box and a circular drum, since the center is a special point.

- Violin String
- Note: This looks like a sawtooth wave, so is less connected to quantum and more related to classical solitons.

- Cymbals
- Note: This shows many modes excited at once, so it is not a simple shape. Quantum-mechanically, this situation is called a superposition.

- Tacoma Narrows Bridge
- Acoustic and vibrational modes are very important in mechanical structures. We will calculate them for atoms and optical cavities.

- Audio in general

- Fundamental Dogma of Spectroscopy, <math>|E_2 - E_1| = h\nu</math>
- Here is Henri Poincaré's Science and Hypothesis, 1905.

[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 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.

- 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.

- 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

## Assigned Homework Problems

- Part 1: Origins (Ch. 1, A, and 2)
- Ch. 1, 1-40 (we'll do 41-44 in class)
- Ch. A, 1-14
- Hint on 12: use i = exp(...)

- Ch. 2, 1-16, 19
- Hint on 1,2, and 4: use y(x) = A exp(ax) + B exp(b x) and check
- Hint on 5: use exp(i omega t) = ...

- Ch. 3, 1-19,24,25,28,29,30,32,35
- Ch. C, all problems except 10; Ch. E, prob. 7; and Ch. F, prob. 1-2,7,11
- We will only multiply and take determinants of 2x2 matrices in this class, but adding larger matrices should be simple.

### Special Assignment for Quiz 4

<math> f_1(x) = e^{ikx} </math> | <math> f_2(x) = 2 i e^{-2x} </math> | <math> f_3(x) = 7 x </math> | <math> f_4(x) = x^2 - 1 </math> | <math> f_5(x) = sin(2 \pi x/a) </math> |

- 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.
- <math>\hat P = -i\hbar \frac{d}{dx}</math>
- <math>\hat S = 3</math>
- <math>\hat R = 2 x \frac{d}{dx} - 1</math>
- <math>\hat H = -c \frac{d^2}{dx^2} </math>

- 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>
- <math>A_1 = </math>
- <math>A_2 = </math>
- <math>A_3 = </math>
- <math>A_4 = </math>
- <math>A_5 = </math>

- Complete the following problems from the text:
- 3-1
- 3-3
- 3-4
- 3-5
- 3-10