WP9 Advanced Mathematical Quantum Mechanics (MA1)
This module offers an overview on advanced chapters of mathematical quantum mechanics. First semiclassical approximations, WKB-calculus, pseudodifferential operators and the Wigner formalism will be discussed. Then basic properties of periodic quantum systems will be presented, among others, the Bloch decomposition, eigenvalues and eigenfunctions of one-body Schr”dinger operators and asymptotic eigenvalue statistics as well as mathematical descriptions of classical and quantized magnetic fields. Next the static problems of many body systems (theory of large atoms for fermionic systems and Bose-Einstein condensation for bosonic systems) will be presented, followed by the dynamical problems of many body systems (scattering theory, asymptotic completeness, correlation functions, BBGKY-hierachy). At the end, disordered quantum systems and Anderson-localization will be discussed. The main goal of this module is to offer an overview of the most successful current research directions for quantum problems that can be tackled by rigorous mathematical methods.