Upon completing the course, students will possess the following skills. They are able to
- explain mathematical derivations and modern formulations of the quantum many-body problem (k2);
- explain important models for the many-electron problem (k2);
- understand and apply approximation methods (k2/k3);
- explain and characterize the mathematical and conceptual challenges of quantum many-body problems (k4);
- understand and discuss current research literature in fields related to the quantum many-body problem, such as material science (k4/k5).
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During the course, students will acquire knowledge about a subset of the following topics of quantum mechanics:
- occupation number formalism and second quantization;
- derivation of quantum field theory by canonical quantization;
- derivation of fermionic and bosonic creation/annihilation operators;
- many-electron problem in 2nd quantization;
- Hubbard model of electrons in solids;
- Hartree-Fock approximation;
- Born-Oppenheimer approximation;
- Greensfunction formalism;
- time-dependent perturbation theory for the many-body problem and Feynman diagrams;
- variational many-body methods;
- microscopic theory of electron-phonon coupling;
- microscopic theory of superconductivity.
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