N-Particle Scattering in a Constant Magnetic Field

We develop the scattering theory for quantum many -particle systems in constant magnetic fields. Scattering theory studies the large-time asymptotic behaviour of the solutions of the time-dependent Schrodinger equation. Its main task is proving asymptotic completeness, i.e., giving a classification of all orbits according to their large -time behaviour. For N interacting quantum particles, one expects that the system either remains stable or breaks up into independent and stable subsystems. In the first part of the thesis we prove asymptotic completeness for one particle and for neutral two-body systems with long-range potentials. In the second part we present the result obtained jointly with C. Gerard --asymptotic completeness for N-particle systems of arbitrary total charge containing no neutral proper subsystems, with long-range interactions.