Physics 215B, Graduate Quantum Mechanics, Winter 2013
Prof. Matthew Fisher
Office: 6105 Broida Hall
Lectures: Monday, Wednesday 2:00-3:15 pm, Phelps 1440
Office Hours: Wednesday 3:30-5:00 pm, Thur 2-3 pm
TA: James Sully
Office: 6126 Broida Hall, 805-285-2643
Office Hours: Tues 2-3, Wed 1-2
Dovetailing with 215A, the broad goal in 215B will be to cover a smattering of topics in single (and few) particle quantum mechanics. In addition to the traditional topics such as symmetries, perturbation theory and scattering, I would like to cover also some more varied (and/or more modern) topics, including reduced density matrices and entanglement, Bell's inequality, quantum computation, and instantons and tunneling via path integrals. Depending on how things go, 215C would be primarily devoted to quantum many-body problems (eg 2nd quantization, lattice and continuum field theories and various possible applications, to condensed matter - eg Bose condensation and superconductivity - and to particle physics - quantized EM field and Dirac theory).
Below is a loose syllabus, subject to modification as the quarter proceeds:
Symmetry in Quantum Mechanics:
- Continous symmetries; Spatial translations, rotations in 2d
- Discrete symmetries; Parity, lattice translations, time-reversal
- WKB (semi-classical)
- Variational method
- Time independent perturbation theory
- Time dependent perturbation theory
- Berry's phase and adiabatic evolution
- Landauer Transport theory for electrical conduction
- Elastic and Inelastic scattering (dynamical structure factor)
- Density matrices; pure versus mixed ensembles
- Entanglement and reduced density matrices
- Bell's Inequality
- Quantum Computation
- Feynman path integrals (instantons and tunneling)
Many-body Topics ...
Textbooks: As in 215A, the "official" textbook for 215B will again be Sakurai, which is a great book covering most of the traditional topics. I also like the quantum mechanics book by Shankar. For topics that are not covered in these books, I will try to suggest other texts and readings.
Homework: Roughly 6-8 homeworks throughout the quarter, available on the course web site. Homework solutions also posted online. You are encouraged to work together on the homeworks.
Exams: Probably none!
Help/feedback: In addition to my office hours and James' office hours, I would be happy to schedule a mutually convenient time to chat about homework or other topics (best arranged by e-mail). I would greatly appreciate feedback on any aspect of the course, anytime throughout the quarter.
Quantum mechanics is a truly remarkable field. Hopefully we can all develop a conceptual intuition for the topic (perhaps dispensing with some of the math?), and have some fun along the way!