These are the slides from Michaelmas 2022. If you want a nice printable version for saving as a PDF, you can use e.g. austen.uk/lectures/many-body-wavefunctions/?print-pdf#/
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- Take place in the Small Lecture Theatre at the Cavendish Laboratory from 09.30-11.00 on Tuesdays and Thursdays.
Product States. Fermi gas. Density, density matrix, and pair distribution.
Landau levels. Laughlin wavefunction. Fractional charge, Fractional statistics.
Quantizing a chain. Ground state displacement fluctuations. statistics.
Heisenberg model. Heisenberg chain. Magnons. Antiferromagnets. Symmetry breaking. Spin wave theory.
Product states and occupation numbers. Creation and annihilation operators. The case of fermions. Representation of operators.
Density correlations. Hanbury Brown and Twiss effect. Hartree–Fock theory.
Tight binding models. Hubbard models and the Mott transition. Superexchange.
Gross–Pitaevskii approximation. Superfluidity. Bogoliubov theory.
Interactions described by perturbation theory. Quasiparticles. Landau Fermi liquid.
Cooper’s problem. BCS theory. The BCS-BEC crossover.
Response functions. Structure factor. Dielectric function. Sum rules.
Some books that you may find useful
- Advanced Quantum Mechanics - A Practical Guide, Nazarov and Danon
- Introduction to Many-Body Physics, Coleman
- Interacting Electrons and Quantum Magnetism, Assa Auerbach
Past exam papers (with solutions)
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