WP0 Mathematical Quantum Mechanics (K1)
This course introduces the basic elements of mathematical quantum mechanics. First the fundamentals of quantum mechanics and the measurement process (EPR-paradox and Bell inequality) and the mathematical basics of unbounded and self-adjoint operators (domain of definition, graphs, adjoints, spectrum, criteria for self-adjointness, spectral theorem, quadratic forms) will be discussed. then Coulomb-Schrödinger operators, the essential spectrum, invariance under compact perturbations and the minimax principle will be presented. This is followed by elements of the theory of many-particle systems (density functional theory, second quantization, fundamentals of quantum field theory) and its applications (e.g. Hartree-Fock approximation, superconductivity and superfluidity). At the end the basics of scattering theory (one-particle problems, the existence of wave operators) will be discussed.