
This course was given from 19972002
Introduction
Advanced Quantum Mechanics for Condensed Matter
is a course for graduate students in experimental
condensed matter physics. The treatment is
necessarily as informal and heuristic as possible.
[These lectures were last given in Michaelmas 2002.]
Synopsis
 Classical Mechanics and its link to Quantum Mechanics.
Lagrangian and Hamiltonian mechanics. Poisson brackets.
Functional derivatives.
Quantum mechanics in a nutshell. Time evolution operators. Spin.
 Second Quantization.
The harmonic oscillator. Creation and
annihilation operators. Quantization of continuous systems.
Quantization of the
electromagnetic field. Tightbinding model. Hofstadter butterfly.
The Hubbard model.
 Representation Theory.
Schrodinger, Heisenberg, Interaction
and Occupation Number Representations. Smatrix. Field operators.
 Path Integrals.
Feynman's sum over histories. Functional
integrals. Link with statistical mechanics. Fluctuationdissipation theorem
(in outline).
 Green's functions.
Singleparticle Green's function. Many body Green's function (outline only).
Spectral density. Quasiparticles.

 Courserelated links

 Quantum theoryrelated links

(Updated: May 2007)
