## Quantum Mechanics II: 314

### Notices

#### We have moved online!

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Here [mp4 file] is the first mini lecture video. This is a test, with administrative information for the rest of the semester, to make sure you can all see the video. **Please let me know** if you have trouble viewing it!

**Lectures**Short video summaries (around five minutes) of the main topics are posted below. I will also be posting the usual lecture notes, although I will be posting them by topic, rather than lecture.**Homeworks**Homeworks are due by email to me. If possible, please try to use an app, such as ``PDFelement'' or ``Image to PDF Converter'' (which should both be free, I believe) to convert your images to PDF files before submitting your homework. Please number your pages to make it easier for us to check that your submissions are complete.**Office hours**I will try to conduct online Q&A office hours at the usual times (Wednesdays and Fridays at 2 pm) via zoom link.**Quick quizzes**I will post quick quizzes on Wednesdays, on the webpage and on Blackboard. They will now be**assessed**and each Quick Quiz is worth ten points. There are five remaining Quick Quizzes, so in total they will be equivalent to one homework. They will form part of your homework score, but are not eligible to be dropped as your lowest homework grade. There will be a discussion board on Blackboard and**within 48 hours**you need to post your answer to one of the questions on the Quick Quiz and a response to someone else's answer (such as giving an example, or more clarification, or suggesting a different way to look at the concept). You will receive ten points for each Quick Quiz.**Midterm 2**The second midterm will be a take-home exam. I will post it on Wednesday April 8 and it is due at midday Friday April 10, by email to me. No late submissions will be allowed, unless by prior arrangement.**Textbook**Thanks to the William & Mary librarians, the textbook is now available through Blackboard.

### 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** 40% Homework, 25% In-class Tests and 35% Final Exam, **or** 40% Homework 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 Yiqi Yang. Make sure you use the correct mailbox!

**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.
- 2/28/20.
- 3/2/20.
- 3/4/20.
- 3/6/20.
- Atoms and mini-lecture.
- Solids and mini-lecture.
- Translations and rotations and mini-lecture.
- Time translation and mini-lecture.
- Parity and mini-lecture.
- Scattering and mini-lecture.
- Partial wave amplitudes and mini-lecture.
- Born approximations and mini-lecture.
- Dirac equation and mini-lecture.
- Course mini-review.

### 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 [and solution].
- Problem Set 5, 3/6/20 [and solution].
- Problem Set 6, 3/23/20 [and solution].
- Problem Set 7, 3/30/20 [and solution].
- Problem Set 8, 4/13/20 [and solution].
- Problem Set 9, 4/20/20
**LAST ONE!**[and solution].

### Exams

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

### Quick quizzes

Quick quizzes are now Discussion Forums on Blackboard. The links below should take you to PDF copies.