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.