Physics 215B, Graduate Quantum Mechanics, Winter 2020
Prof. Matthew Fisher
email: email@example.com ;
Office: 2305 Kohn Hall
Lectures: Monday, Wednesday 11:00-12:15 pm, Arts 1353
Office Hours: Wednesday, 2-3pm
Find the course web site thru my personal web site: https://www.kitp.ucsb.edu/mpaf
Grader/TA: Yaodong Li
Office: 6234 Broida Hall
Office Hours: Tuesday 2-3pm
Textbooks: The "official" textbook for 215B is Sakurai/Napolitano (2nd edition). There are many good QM books - including Shankar, Gottfried/Yan, Landau-Lifshitz, among others. However, I am hoping to include some more modern topics (e.g. Quantum Ising model and Majorana Fermions) which are not in these books. I will try to suggest other reading/books when relevant.
Homework: Roughly 5-6 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: None. Unless requested!
Help/feedback: In addition to my office hours and Yaodong's 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.
SYLLABUS for 215B
Path Integral Formulation of Quantum Mechanics:
- Real time and Euclidian path integrals
- Instantons and tunneling
- Path integrals for identical particles
- Quantum Information, Complexity and Parallelism
- Quantum Algorithms - Deutsch algorithm, Grover Algorithm
- Quantum Error Correction
(Symmetry in Quantum Mechanics)
- Continous symmetries; Spatial translations, rotations and angular momentum (briefly)
- Discrete symmetries; Parity, lattice translations, time-reversal
- 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)
Lattice Quantum Field Theory:
- Quantum Transverse Field Ising model
- 1d Quantum Ising Model and Majorana Fermions