Physics 215A, Graduate Quantum Mechanics, Fall 2014
Prof. Matthew Fisher
email: firstname.lastname@example.org ;
Office: 1118 Kohn Hall
Lectures: Tuesday, Thursday 11:00-12:15 pm, Phelps 1508
Office Hours: Tuesday, Thursday 2:30-3:30 pm
Find the course web site thru my personal web site: http://www.kitp.ucsb.edu/mpaf
Grader/TA: Alex Rasmussen
email: email@example.com ;
Office: 6218 Broida Hall
Office Hours: Wed 2-4pm
Textbooks: The "official" textbook for 215A is Sakurai/Napolitano (2nd edition), which is a good book covering many traditional topics. And of course there are a number of other such books - including Shankar, Gottfried/Yan, Landau-Lifshitz, among others. However, I am hoping to include some more modern topics (eg entanglement entropy, quantum computing) which are not in these books. I will try to suggest other reading/books when relevant.
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: Perhaps a Take-Home final.
Help/feedback: In addition to my office hours and Alex' 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, early on?), and have some fun along the way!
- Linerar vector spaces, dual spaces, Dirac notation and operators
- Eigenvectors/eigenvalues of Hermitian operators
- Projection and Completeness
- Unitary Transformation and Representations
- Compatible and Incompatible Operators
Formulation of Quantum Mechanics:
- U-Process: Dynamics, Unitary Time Evolution and the Hamiltonian Operator
- R-Process: Measurements and State Reduction
2-State Quantum System(s):
- Pure versus mixed ensembles
- Quantum Statistical Mechanics
- Thermal Entropy
- Entanglement entropy and Non-locality
- Local Measurements and disentangling
- Bell's Inequality
- Schrodinger's Cat
- No-clone Theorem
- Quantum Information, Complexity and Parallelism
- Q-bit formalism
- Quantum Algorithms - Deutsch algorithm, Grover Algorithm
- Single Quantum particle - tight binding model, translational symmetry and the continuum limit
- Many Quantum particles: 2nd Quantization for Bosons and Fermions
- Lattice Quantum Field Theories