Physics 221B:
Graduate Quantum Mechanics II

Syllabus may be modified as course progresses.

Identical Particles and second quantization

  • Review of Harmonic Oscillator
  • Creation and annihilation operators
  • Indistinguishability,Many particle states, Fock basis
  • Symmetry
    • Fermions and Bosons
    • Maxwell Boltzmann, Fermi-Dirac, Bose-Einstein distributions
    • Slater Determinant
    • Examples: Many particles in a box, 2 e-, Helium, rotational lines of molecules
    • Scattering and Exchange terms
    • Young Tableaux
  • Second Quantization
    • dynamical variables, continuous labels, dynamics, momentum space
    • 1 particle and pair correlation functions

Applications of Second Quantization

  • Correlation functions (simple example)
  • Angular momentum of many particle systems
  • Spin Waves (spontaneous symmetry breaking)
  • Quantum statistics (operator version)
  • Perturbation Theory: Mean Field and Thomas Fermi Theory, Hartree Fock
  • Pairing
    • Independent pair model
    • Hubbard Model: strong and weak coupling
    • Bogoliubov transformations
    • Superconductivity
  • Bose Einstein Condensates (homework 6)
  • Anyons and Fractional Statistics

Photons and the electromagnetic field

  • Maxwell's equations in terms of gauge fields
  • Electromagnetism in the absence of charges: classical and quantum treatment
  • collection of photons vs. classical electromagnetic fields
  • non-rel matter plus radiation
    • Radiative transitions
    • Dipole, Lifetimes, Detailed Balance, Thomson scattering
    • Current source
  • Casimir Effect

Relativistic Wave Equations

  • Lorentz and Poincare transformations in quantum mechanics
  • Klein Gordon Equation, current, quantization and anti-particles
  • Dirac Equation, current
  • spinors, gamma matrices, basis functions
  • angular momentum, spin, helicity
  • quantization, QED
  • gauge invariance
  • Yukawa interaction, first order perturbation theory
  • Higher orders in perturbation theory

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