Quantum theory of many-body systems

Dr. Irina Petreska, Professor

Course content:

1. Introduction. Secondary quantization. Kinetic energy, spin, particle density and current density operator in secondary quantization. Coulomb operator in secondary quantization. Hartree-Fock method in secondary quantization. 

2. Electronic correlations. General form of the many-particle electron-ion Hamiltonian. Free electron gas model. Electronic interactions within the framework of perturbation theory. Electron gas in one, two and three dimensions. 

3. Non-stationary problems. Temporal evolution of conditions. Schrödinger's approach. Heisenberg's approach. Interactions. Unitary time evolution operator. Linear response. Time-dependent generation and annihilation operators. Green's functions.  

4. Secondary quantization and statistical mechanics. Spin lattice models. Ising's model. Heisenberg model. Hubbard model. Non-interacting limit.

5. Magnetism. Introduction to the quantum theory of magnetism. Ferromagnetism. Heisenberg model of ion ferromagnets. Stoner-Hubbard model of metallic ferromagnets.

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