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Spring 2009: Quantum Mechanics II

Instructor: Philip Stamp Contact:
  • Office: Hennings 311A
  • office phone: 604-822-5711

Lectures: (tentatively) 12:30-14:00 on Mon, Wed and Fri, in Hennings 302. Precise schedule to be decided.

Grading: (tentatively)

  • 40%: assignments
  • 60%: final exam

Syllabus: pdf file

What follows is a rough guide to what will be in this course. There is no set book for the course -- there are of course many books at roughly the level of this course, and a list of some good ones is given below. However the course notes, supplemented by selected reading, should suffice as background material. The course will include many examples from different fields of physics. The level of the course will depend to some extent on the audience.

(1) BASICS

  • Classical Physics: Hamiltonians & Lagrangians, & Symmetries
  • Wave-functions and density matrices; Schrodinger eqtn.
  • Quantum Measurements & Entanglement
  • Basic Theory of Path integrals - derivation of Schrodinger eqtn

    (2) FERMIONS & BOSONS

  • Statistics: fermions, bosons, & anyons
  • 2nd quantization; coherent states

    (3) PERTURBATION THEORY

  • Time-independent theory: expansion in small parameter; diagrammatic representation
  • Level repulsion
  • Scattering theory: Born approximation, S-matrix & T-matrix; Resonant scattering, bound states
  • Time-dependent perturbation theory: Adiabatic & sudden limits; Fermi Golden rule
  • Landau-Zener formula, Berry phase; asymptotic results

    (4) SEMICLASSICAL APPROXIMATIONS

  • Classical & Quantum orbits; trace formulae; quantum chaos
  • WKB and Tunneling, and other non-perturbative effects; topological phase

    (5) SPIN & ANGULAR MOMENTUM

  • Spin & Angular momentum algebra
  • Scattering off central fields; applications in atomic, nuclear, & condensed matter physics
  • Einstein-Podolsky-Rosen effects; separability; quantum teleportation
  • Coherent states & path integrals for spin. Spin tunneling & topological spin phase

    SOME USEFUL BOOKS

  • AB Migdal Qualitative Methods in Quantum Theory
  • LD Landau, EM Lifshitz Quantum Mechanics
  • K Gottfried Quantum Mechanics
  • RP Feynman AR Hibbs Quantum Mechanics & Path Integrals
  • JJ Sakurai Advanced Quantum Mechanics
  • LS Schulman Techniques & Applications of Path Integrals
  • LI Schiff Quantum Mechanics
  • RP Feynman, RB Leighton, M Sands Feynman lectures on Physics, vol III