## Quantum Mechanics II: PHYS 314

[Spring 2022]

### Notices

This semester could potentially 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. There are lot of good mental health resources available online, such as virusanxiety.com.

The final will be a take-home exam, posted before 9 am on Monday May 9 and due at 12:00 noon on Friday May 13.

### Course details

**Class schedule:** In-person classes take place twice a week in Small Hall 233.

**Office hourse:** Wednesday 12-1 pm (in-person or via Zoom, depending on the week) and Thursday 2-3 pm in person. My office is 326C Small Hall.

**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). It helps to have taken Introduction to Mathematical Physics (PHYS 254), but it is not a prerequisite.

**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.

### 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:

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