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
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.
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.) , (Addison Wesley, 1994)., and 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, (Springer, 1999). This text does a very nice job treating second quantization (Chapters 1, 2 and 3) and also treats relativistic quantum mechanics (Chapters 5 and 6). The full text is available online through Queens. The direct link is: http://www.springerlink.com/content/q2223h/#section=140498&page=1&locus=0.
- 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.