Physics 215B (Winter 2013)

SYLLABUS: 

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 

 

Approximation methods:

• WKB (semi-classical)
• Variational method
• Time independent perturbation theory
• Time dependent perturbation theory
• Berry's phase and adiabatic evolution

 

Scattering:

• Landauer Transport theory for electrical conduction
• Elastic and Inelastic scattering (dynamical structure factor)

 

Miscellaneous: 

• 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 ...

 

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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.