New approach to quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field

For a fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schrödinger operator with a constant magnetic field and an axisymmetrical electric potential V. Asymptotic expansions for the resolvent of the Hamiltonian H m ?=?H om ?+?V are deduced as the spectral parameter tends to the lowest Landau threshold E 0. In particular it is shown that E 0 can be an eigenvalue of H m . Furthermore, asymptotic expansions of the scattering matrix associated with the pair (H m , H om ) are derived as the energy parameter tends to E 0.