Physics 443 - Spring 2008 - Syllabus

General Principles

• Wave Particle Duality
• Schrodinger Equation
• Conservation of Probability
• Hidden variables
• Expectation values
• Ehrenfest's theorem
• Probability current
• Hermitian operators

Solutions to Schrodinger's Equation in 1-dimension

• Separation of variables
• Stationary states
• Free Particle
  • Wave packets
  • Group velocity
• Infinite square well
  • Symmetry
  • Orthogonality
  • Nodes
  • Completeness
• Harmonic oscillator
  • Ladder operator
  • Normalization
  • Coherent state
• Linear potential (bouncing ball)
  • Dimensional analysis
  • Airy function
• Delta function potential
  • Boundary conditions
  • Scattering

Linear Algebra

• Time dependence of expectation values
• Conservation of energy
• Uncertainty principle
• Minimum uncertainty wave packet
• Generators, translations, rotations, time displacement
• Non conservation of probability and complex potential
• Neutral Kaon
• Neutrinos

WKB approximation

• Turning points
• Decay of radioactive nuclei
• Connection Formulae

Spherically symmetric potentials

• Angular momentum
• Harmonic oscillator in 2 and 3 dimensions
• Spin
• Rotations
• Magnetic moment in a magnetic field
• Angular momentum eigenfunctions in spherical coordinates

Coulomb potential

• Hermite polynomials
• Degeneracy

Gauge transformations

Entangled states

Identical Particles

Stationary State Perturbation Theory

Variational Method

Time dependent Perturbation Theory

Dirac Equation