Phys3707 Intermediate Quantum Mechanics -- Many Body Physics
Instructor:
E.S. Swanson
404 Allen Hall
4-9057 swansone@pitt.edu http://fafnir.phyast.pitt.edu/IQM/
class meets Mondays and Wednesdays 11:00 - 12:15, 419 Allen Hall.
Office Hours: I will keep no official hours, drop in any time!
required text:
- A. Fetter and J.D. Walecka, Quantum Theory of Many Particle Systems. ($25 at Barnes and Noble)
Additional texts:
Some good introductory texts:
- R.D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem
- N.H. March, W.H. Young, and S. Sampanthar, The Many-Body Problem in
Quantum Mechanics
- R. Landau, Quantum Mechanics II
And some more advanced texts:
- J.P. Blaizot and G. Ripka, Quantum Theory of Finite Systems
- P. Ring and P. Schuck, Nuclear Many-Body Problem
- J. Negele and H. Orland, Quantum Many Particle Systems
Marking Scheme: to be discussed in class.
Syllabus:
- Introduction [MYS ch1, FW ch1, M ch0]
- many particle systems, single particle states, Fermi sea,
Hartree mean field method
- Second Quantization [MYS ch3, FW ch1, L ch19+26, M ch7]
- occupation number formalism, one body and two body operators, fermions
and bosons, canonical transformations, particle-hole formalism, field operators
- Perturbation Theory and Green's Functions [MYS ch4+10, FW ch 3, L ch, M ch8-10]
- Brillouin-Wigner and Rayleigh-Schroedinger perturbation theory, Goldstone theorem, adiabatic switching, time evolution, scattering theory, Wick's theorem,
Green's functions, propagators, spectral function, Dyson equations
- Fermi Fluids [FW Ch 4+5, M ch 12+13, MYS ch5]
- Coulomb screening, Gell-Mann -- Brueckner theory, ring diagrams, collective modes and plasmons, effective mass and renormalization, particle lifetimes,
random phase approximation
- Light and Matter [Sakurai ch1+2, L ch20+21]
- review of E&M, gauge invariance, Coulomb gauge,
photons, spontaneous emission, black body radiation,
Kramers-Heisenberg formula, Thomson, Compton, Rayleigh scattering,
photo-electric effect
- Spin Systems [class notes]
- spin, para- and ferromagnetism, Heisenberg model, Ising model, spin waves, momentum space, Hubbard model, t-j model, critical phenonena, renormalization group, universality.
- Bosonic Systems [MYS ch 8]
- phonons, liquid 4He, density fluctuations, Bogoliubov model,
rotons, zero sound
If time permits we will touch on superconductivity, nuclear matter, and the finite
temperature formalism.
Problem Sets