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Advanced Quantum Mechanics for Condensed Matter
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This course was given from 1997-2002
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. Tight-binding model. Hofstadter butterfly.
The Hubbard model.
- Representation Theory.
Schrodinger, Heisenberg, Interaction
and Occupation Number Representations. S-matrix. Field operators.
- Path Integrals.
Feynman's sum over histories. Functional
integrals. Link with statistical mechanics. Fluctuation-dissipation theorem
(in outline).
- Green's functions.
Single-particle Green's function. Many body Green's function (outline only).
Spectral density. Quasiparticles.
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- Course-related links
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- Quantum theory-related links
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(Updated: May 2007)
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