Phys314 — Quantum Mechanics II

Purpose of this course

In this second semester of Quantum Mechanics we will broaden our understanding of the theory, considering techniques that can lead us to approximate solutions of more complicated systems. Application of quantum formalism to descriptions of atomic systems, solid state systems, nuclei and other subatomic particles will be presented.

Class Schedule

Tuesdays and Thursdays, 9.30am — 10.50am in Small Hall 233.

Office Hours

Fridays 1.30pm — 3.00pm in Small Hall 328C.

Lecture Notes

I’ll post the lecture notes i'm working from on this website as we go along. Hopefully this means you can do less writing and be a bit more focussed during lecture time. Please let me know of any errors you spot in the notes.

Problem Sets

There will be regular problem sets on the material we cover in lectures. These are a very important part of the course, almost certainly more important than listening to your lecturer waffle on. Sitting through lectures may make you feel like you have learned something, but you don’t really know until you try to use the techniques you think you have learned. The only way to become comfortable with the tools is through practice.

I intend the problem sets to be pedagogic, and in some cases will fill in important topics that we don't have time to cover in lectures. There will be one problem set roughly every week, with a few gaps.

I would strongly suggest that you should work on the problems first on your own, but if you remain stuck you can confer with your peers or get help from me. I furthermore would strongly suggest that you use search engines or AI tools as a last resort only after you've exhausted your own efforts, conferred with your peers, and asked me for help — the experience of finding your way to a solution is a powerful learning process, and shortcutting it can cost you in the long-term. In addition (as with any purported solution to a problem) you should check carefully that any AI-generated answer makes sense.

Anything you present in a solution must reflect your understanding at a level where if I asked you to explain it to me on the blackboard, you would be able to. Simply copying someone else's solution without understanding it would not meet this bar, and will be considered to be cheating.

Because I will (try to) provide solutions promptly (to help you understand anything you might have missed while the problems are still fresh in your mind), significant extensions to problem set deadlines will not be possible. If you need a short extension of a few hours, you may request it in advance of the deadline. Large-scale unexpected incidents can be handled individually, please get in touch by email and we will arrange some accommodation.

The problem sets and deadlines will be posted below.

Exams

There will be a midterm exam (in class on March 5th) and a final exam (to be scheduled).

Books

We'll largely follow Griffiths & Schroeter Introduction to Quantum Mechanics (Third Edition) which serves as a recommended text for this class. There are many good Quantum Mechanics books out there targeted at the undergraduate and graduate levels. Some that I am familiar with, which you might be interested in looking at, are:

• Gasiorowicz Quantum Physics. A nice compact book aimed at undergraduates, with clear notation and good problems. Was my preference when I was learning QM for the first time.
• Tong Quantum Mechanics. Lectures on Theoretical Physics, Volume 3. David Tong is a master of pedagogic presentation, and explains many things books often skip over. Based on lectures given to students in a mathematics department, but doesn't assume a great deal of advanced math skill. The only book in this list which has a decent discussion of foundations of quantum mechanics and quantum computing, covering topics like entanglement, measurement and decoherence, which are slightly beyond the scope of this class.
• Feynman The Feynman Lectures on Physics Volume III. Designed to be taught to undergraduate freshmen! Not formal at all, assumes very little mathematics. Beautifully written, and fun to read, but not really a textbook in the usual sense of the word.
• Sakurai Modern Quantum Mechanics. Newer editions have been updated by Jim Napolitano. Aimed at graduate students, but gentle enough for undergrads if your math is reasonably strong.
• Gottfried & Yan Quantum Mechanics: Fundamentals. Definitely designed for graduate students, assumes strong math skills, gets through the basic material quite quickly, more formal in some places, but quite a few nice applications.

There are many other textbooks out there, i'm just less familiar with them. Make sure you have access to at least one that you're comfortable with. There might be minor notational differences with respect to the lectures, but that's something we all have to get used to anyway.

Topics

• Review of material covered in the first semester
• Perturbation Theory
• Variational Approach
• Systems of Identical Particles
• Quantum Mechanics of Atoms
• Quantum Mechanics of Solids
• Time-dependent Interactions
• Scattering
• Properties of Quantum States

We'll get through as many of these topics as time allows.

Grading

The final letter grade will be computed using input from

Problem Sets: 30%, Midterm Exam: 20%, Final Exam: 50%.

Lecture Notes

Problem Sets