New Approach to Quantum Scattering Near the Lowest Landau Threshold for a Schrödinger Operator with a Constant Magnetic Field

Abstract

For a fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schrodinger 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 E0. In particular it is shown that E0 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 E0.