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, 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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