Physics 221B:
Graduate Quantum Mechanics II
Syllabus
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, FermiDirac, BoseEinstein 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
 nonrel 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 antiparticles
 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
