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PHY 6646 - Spring 2004
Topics Covered

The subject matter of the course is defined by the content of the lectures plus all reading assignments announced in class. The main topics are listed below in the order they were covered. Each topic is cross-referenced to the most closely related section(s) of Shankar ("Sh"), Ballentine ("Ba"), Merzbacher ("Me"), and/or Sakurai ("Sa").

Addition of Angular Momenta (continued from Fall 2002)
    Scalar, vector, and tensor operators (Sh15.3)
    Irreducible tensor operators (Sh15.3, handout)

Particle in an Electromagnetic Field
    Charged particle in an EM field: general formalism (Sh18.4, Ba11.2)
    Charged particle in a uniform electric field (Me7.2)
    Charged particle moving in a uniform magnetic field (Ba11.3)
    The Aharanov-Bohm and related effects (Ba11.4, Sh18.4, handout)
    Orbital and spin magnetic moments (Sh14.4)
    Spin dynamics (Sh14.4, Ba12.1)
    Spin-1/2 in a magnetic field (Sh14.4)

The Variational Method
    Variational formulation of the eigenvalue problem (Ba10.6)
    The variational method (Ba10.6, Sh16.1)
    Variational theorem for the lowest eigenvalue (Sh16.1)
    Variational approximations for higher eigenvalues (Sh16.1, Me8.2)

The WKB Method
    The WKB approximation (Me7.1, Sh16.2)
    The connection formulae (Me7.2, Sh16.2, handout)
    Bound states (Me7.3, Sh16.2)
    Tunneling though a barrier (Me7.4, Sh16.2)

End of material tested on Exam 1

Time-Independent Perturbation Theory
    Rayleigh-Schrodinger perturbation theory (Sh17.1, Sh17.2)
    Degenerate Rayleigh-Schrodinger perturbation theory (Sh17.3, handout)
    Near degeneracy (Ba10.5)
    Brillouin-Wigner perturbation theory (Ba10.5, handout)

Time-Dependent Perturbation Theory
    General formalism (Ba12.5)
    First-order perturbation theory (Sh18.2)
    Harmonic perturbations (Sh18.2)
    Interaction of atoms with electromagnetic radiation (Ba12.6)
    Induced transitions between discrete states (Ba12.6)
    The photoelectric effect (Sh18.5, handout)
    Second-order time-dependent perturbation theory: virtual transitions, energy shifts, and decay widths (handout)

End of material tested on Exam 2

Scattering Theory
    Basic ideas (Sh19.2)
    Scattering theory (Sh19.4, Sa7.1, Me13.3)
    Born approximation (Sh19.3-4)
    Method of partial waves (Sh19.5)
    Two-particle scattering (Sh19.6)

Identical Particles
    Permutation symmetry (Ba17.1)
    Indistinguishability of identical particles (Ba17.2)
    The symmetrization postulate (Ba17.3, Sh10.3)
    Second quantization: creation and annihilation operators (Ba17.4, Me21.2, handout)

End of material tested on Final Exam

    Quantization of the electromagnetic field (Me23.1, Sh18.5)

Introduction to Relativistic Quantum Mechanics
    The Klein-Gordon and Dirac Equations (Sh20.1)
    The emergence of spin (Sh20.2)
    Antiparticles (Sh20.3)

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Kevin Ingersent / ingersent@phys.ufl.edu
Last modified: Apr 28, 2004