**Phys 825 Advanced Quantum Mechanics (Fall 2020)**

This is the course webpage for PHYS825 when I am teaching it — note that a different instructor will be teaching this class in Fall 2021.

**Instructor: **Prof. Aaron Vincent

## Homework Assignments

## Course notes

Typed notes

More on spherical basis

Intro to scattering and Feynman diagrams

This wikipedia link gives a nice summary of Feynman diagrams in QED

## General Course Information

**Required text:** You are not required to purchase a textbook. In addition to my own classnotes, I will email you a link to the more detailed notes by** M. Dignam.**

### List of Topics to be Covered

- Review: Hibert spaces, etc.
- The path integral formalism of quantum mechanics
- Symmetries and invariance in quantum theory
- Second quantization, many-particle systems and Hartree-Fock theory
- Relativistic quantum mechanics and the Dirac equation

### Things you should be familiar with

We will go over some of this in the first few weeks to remind ourselves how it works. If you require more background material I can provide notes from PHYS 345, the highest undergraduate-level course in QM taught at Queen’s.

- The Dirac bra/ket formalism, Hilbert spaces, eigenvalues & eigenkets, operators.
- The Schrödinger equation and its solutions: harmonic oscillator, square well, hydrogen atom, quantum tunnelling.
- Perturbation theory (time-dependent and time-independent) and variational methods of solving the Schrödinger equation.
- Angular momentum: spin 1/2 systems, spinors, addition of angular momenta. Clebsch-Gordan coefficients.

### Supplementary Material

Your main source of material should be the lectures and the notes that I post. Because there are several rather distinct topics covered in this course, there is not one text that covers them all at the appropriate level. However, here are a number of texts that cover some of the material. Sakurai is available electronically through the library. I list the others mainly for completeness:

**Sakurai***,**Modern Quantum Mechanics*(2nd Ed.)**Sakurai & Napolitano***Revised edition*, reprinted 2017. I’m mostly (but not exclusively) using this when not following M. Dignam’s notes. On reserve in the library.

**Merzbacher***Quantum Mechanics*(Third edition) . Wiley, 1998.**Marchildon,***Mécanique Quantique*, Bibliothèque des universités. De Boeck Supérieur, 2000.

**Cohen-Tannoudji, Diu**and**Laloe***,**Quantum Mechanics*Vols. I and II, (Wiley, 1977). This is useful for some of the symmetry material and for review of the Dirac formalism. Some people love it, I find it way too verbose.*Dirac,**Lectures on Quantum Mechanics*and*Principles of Quantum Mechanics***.**Insight into the origin of QM from Dirac himself.*Lectures*on reserve at the library, both decently easy to find online.**Shankar**Principles of Quantum Mechanics,*,**1977.*A decent treatment of the basics.**Schwabl,***Advanced Quantum Mechanics*,**Schwartz:***Quantum Field Theory and the Standard Model*. This is the reference I use for much of our relativistic QM treatment in the final part of the course.**Srednicki,***Quantum Field Theory*. Draft available for free on Srednicki’s website: https://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf. Beware typos and metric convention.**P. Kaye, R. Laflamme and M. Mosca,***An Introduction to Quantum Computing*, (Oxford 2007). This is the main source for M. Dignam’s quantum computing portion of the course, which cover much of chapters 1, 3, 4, 5 and 6. We probably won’t get to this material. This text is available online through Queen’s library. The link is: http://lib.myilibrary.com/Open.aspx?id=75761&loc=&srch=undefined&src=0.

## Evaluation

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