Physics 215B/C, Graduate Quantum Mechanics, Winter/Spring 2019
Prof. Matthew Fisher
email: mpaf@kitp.ucsb.edu ;
Office: 2305 Kohn Hall
Lectures: Monday, Wednesday 11:00-12:15 pm, Phelps 3505
Office Hours: Wednesday, 2-3pm
Find the course web site thru my personal web site: http://www.kitp.ucsb.edu/mpaf
Grader/TA: Yaodong Li
email: lyd@physics.ucsb.edu
Office: 6124 Broida Hall
Office Hours: Tuesday 2-3pm
Textbooks: The "official" textbook for 215B/C 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 6-7 homeworks throughout each 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.
215B Problem Sets
215B Problem Solutions
215C Problem Sets
215C Problem Solutions
SYLLABUS for 215B
2-State Quantum System (brief review):
- Measurements
- Dynamics
Density Matrices:
- Pure versus mixed ensembles
- Quantum Statistical Mechanics
- Thermal Entropy
Entanglement:
- Reduced Density Matrix
- Schmidt Decomposition
- Entanglement entropy and Non-locality
- Local Measurements and disentangling
Quantum "Paradoxes":
- Bell's Inequality
- Schrodinger's Cat
- No-clone Theorem
Quantum Computing:
- Quantum Information, Complexity and Parallelism
- Q-bit formalism
- Quantum Algorithms - Deutsch algorithm, Grover Algorithm
Symmetry in Quantum Mechanics:
- Continous symmetries; Spatial translations, rotations and angular momentum (briefly)
- Discrete symmetries; Parity, lattice translations, time-reversal
Approximation methods:
- Time Independent Perturbation Theory
SYLLABUS for 215C
Approximation methods: (cont'd)
- Time dependent perturbation theory
- Berry's phase and adiabatic evolution
Scattering Theory
- Landauer Transport theory for electrical conduction
- Elastic and Inelastic scattering (dynamical structure factor)
Path Integral Formulation of Quantum Mechanics:
- Real time and Euclidian path integrals
- Instantons and tunneling
- Path integrals for identical particles
Lattice Quantum Field Theory:
- Quantum Transverse Field Ising model
- 1d Quantum Ising Model and Majorana Fermions
Continuum Quantum Field Theory:
- Many Quantum particles: 2nd Quantization for Bosons and Fermions
- BEC and weakly interacting Bosons
- Fermi Gas
- Quantizing the Electro-Magnetic field
- Dirac model in 1d, 2d and 3d