## Quantum Mechanics II: PHYS 314

[Spring 2021]

### Notices

This semester is going to be another challenging one. Look after yourself and those around you! This is a very stressful and difficult time for everyone, so please be compassionate with yourself and those around you, and look after yourself. Don't forget that Social Distancing doesn't have to mean Social Isolation! There are lot of good mental health resources available online, such as virusanxiety.com.

Our first meeting of the semester will be **09:30-10:50 am** on **Thursday January 28** via Zoom. This will largely be an overview of how the course will look and what you can expect.

### Course details

**Class schedule:** In-person classes take place once a week in Small Hall 111, starting on **Thursday** February 11 **09:30-10:50**. The first two weeks of semester will be completely online and we will meet via Zoom.

**Textbook:** We will cover a wide variety of topics and no textbook covers them all. A lot of the material will come Griffiths and Schroeter's *An Introduction to Quantum Mechanics* (3^{rd} edition). This was the textbook you used for PHYS 313, but it is only recommended, not required. I will post my lecture notes here each week.

**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** 40% Problem Sets, 25% Midterm Tests and 35% Final Exam, **or** 40% Problem Sets and 60% 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 Jack Jackson, but please email your solutions **to me**.

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

**Office hours:** **Tuesdays 09:30-10:50 am** or by arrangement. Office hours are via Zoom.

### 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:

- Path integrals in quantum mechanics
- Symmetries and conservation laws.
- Spin and statistics.
- Relativistic quantum mechanics.
- Scattering.
- Variational methods.
- Time-independent perturbation theory.
- Fine and hyperfine structure of hydrogen.
- Time-dependent perturbation theory.

### Syllabus

A draft syllabus can be found here (pdf). Expect it to be updated as the semester progresses!### Lecture notes

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

### Summary videos

The links below should take you to short (mp4) video summaries for each week.

- Video 1 and Video 2.
- Video 1 and Video 2.
- Video 1, Video 2, and Video 3.
- Video 1, Video 2, and Video 3.
- Video 1 and Video 2.
- Video 1, Video 2, Video 3, Video 4, Video 5, Video 6, Video 7 Video 8, Video 9, Video 10, Video 11, and Video 12.
- Video 1, Video 2, and Video 3.
- Video 1.
- Video 1 and Video 2. And extra Tuesday video.
- Video 1, Video 2, and Video 3.

### 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 Haoyue Jiang (hjiang06) for questions about grading.

- Problem Set 1, 2/4/21 and solutions.
- Problem Set 2, 2/11/21 and solutions.
- Problem Set 3, 2/18/21 and solutions.
- Problem Set 4, 3/5/21 and solutions.
- Problem Set 5, 3/11/21 and solutions.
- Problem Set 6, 3/18/21 and solutions.
- Problem Set 7, 4/08/21 and solutions.
- Problem Set 8, 4/15/21.

### Quick quizzes

The links below should take you to PDF copies of our Thursday Quick Quizzes.

- Quick Quiz 1.
- Quick Quiz 2.
- Quick Quiz 3.
- Quick Quiz 4.
- Quick Quiz 5.
- Quick Quiz 6.
- Quick Quiz 7.
- Quick Quiz 8.
- Quick Quiz 9.
- Quick Quiz 10.

### Exams

The links below should take you to PDF copies of the exams.