## Quantum Mechanics II: 314

### Notices

### Course details

**Class schedule:** Classes take place in Small Hall 233, **Monday**, **Wednesday**, and **Friday 12:00-12:50**. The first class will take place Wednesday January 22^{nd}.

**Textbook:** We will use Griffiths and Schroeter's *An Introduction to Quantum Mechanics* (3^{rd} edition). This was the textbook you used for PHYS 313. I will make my (hand written) notes available here after class.

**Prerequisites:** Modern Physics (PHYS 201) and Classical Mechanics (PHYS 208) are prerequisites for this course, as is a strong command of the material from the first semester of quantum mechanics (PHYS 313).

**Instructor:** Chris Monahan (he/his/him), Small Hall 326C. Email: cjmonahan'at'wm.edu.

**Course grading:** The grades will be calculated based on **either** 25% Homework, 45% In-class Tests and 30% Final Exam, **or** 25% Homework and 75% Final Exam. For each student, the final grade will be calculated using both equations, and the result with the larger numerical grade will be the one used to determine the letter grade. The course grader is Yiqi Yang.

**Problem sets** Homeworks will be posted on Monday before class and are due midday the following Monday. **I will drop the lowest grade on your weekly homework.**

**Office hours:** **Wednesdays and Fridays 2:00-3:00 pm** or by arrangement.

### Course description

How do we describe our Universe at very small length scales? How do we explain why hydrogen looks the way it does, or, for that matter, why the elements line up in the periodic table so neatly? The answer, of course, is **quantum magic mechanics**!

We will start to unravel some of this quantum magic by building on the first semester of quantum mechanics (PHYS 313) and introducing new techniques for systems for which we do not have exact solutions (that is, basically everything). This includes the detailed structure of hydrogen energy levels, helium atoms and nuclei, collections of identical particles, quantum scattering effects, and systems that evolve with time. We will briefly introduce concepts that appear throughout modern theoretical physics, such as the deep relationship of symmetries and conserved quantities, and a quick peek at quantum field theory, the mathematical framework that brings together quantum mechanics with special relativity, which explains all fundamental particles in the observable Universe.

We will cover:

- Time-independent perturbation theory.
- Fine and hyperfine structure of hydrogen.
- Time-dependent perturbation theory.
- Variational methods.
- Spin and statistics.
- Symmetries and conservation laws.
- Scattering.

This is most of the second half of the textbook, from Chapter 5 to Chapter 11, excluding Chapter 9, although not quite in order.

### Syllabus

Can be found here (pdf).### Lecture notes

The links below should take you to PDF copies of the lecture notes for each class.

- 1/22/20.
- 1/24/20 [extra notes on Eq. 7.11 here].
- 1/27/20.
- 1/29/20.
- 1/31/20.
- 2/3/20.
- 2/5/20 [plus brief extra notes on commutator algebra for angular momentum operators].
- 2/7/20.
- 2/10/20.
- 2/12/20.
- 2/14/20.
- 2/17/20.
- 2/19/20.
- 2/21/20 [plus selected solutions to suggested problems here].
- 2/26/20.

### Problem sets

The links below should take you to PDF copies of the problem sets for each week. Each problem set is graded out of fifty points. Contact Yiqi Yang (yyang25) for questions about grading.

- Problem Set 1, 1/27/20 [and solution].
- Problem Set 2, 2/03/20 [and solution].
- Problem Set 3, 2/10/20 [and solution].
- Problem Set 4, 2/24/20.

### Midterms

The first midterm of the course will take place on **Monday 24 February**. The link below should take you to a PDF copy of last year's first midterm. Note that I did not teach the course last year, nor set the exams.

- 2019 Midterm 1 [and solution].