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Advanced Quantum Mechanics for Condensed Matter

This course was given from 1997-2002


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.]


  • 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.

Course-related links
Quantum theory-related links
(Updated: May 2007)
Email: s dot blundell at physics.ox.ac.uk