
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 crossreferenced 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 AharanovBohm and related effects (Ba11.4, Sh18.4,
handout)


Orbital and spin magnetic moments (Sh14.4)


Spin dynamics (Sh14.4, Ba12.1)


Spin1/2 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
TimeIndependent Perturbation Theory

RayleighSchrodinger perturbation theory (Sh17.1, Sh17.2)


Degenerate RayleighSchrodinger perturbation theory (Sh17.3,
handout)


Near degeneracy (Ba10.5)


BrillouinWigner perturbation theory (Ba10.5,
handout)

TimeDependent Perturbation Theory

General formalism (Ba12.5)


Firstorder 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)


Secondorder timedependent 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 (Sh19.34)


Method of partial waves (Sh19.5)


Twoparticle scattering (Sh19.6)

Identical Particles
Introduction to Relativistic Quantum Mechanics

The KleinGordon and Dirac Equations (Sh20.1)


The emergence of spin (Sh20.2)


Antiparticles (Sh20.3)

