Scatteing for hydrogen-like systems in a constant magnetic field ∗∗

We prove asymptotic completeness for a system of two particles with opposite charges interacting via a long-range potential decaying faster than |r|^-1/2 at infinity in a homogeneous magnetic field. In particular, our result implies asymptotic completeness for the hydrogen atom with finite nuclear mass in a uniform magnetic field, which has not been proven previously.