Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field

For 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 $V$. In various, mostly fairly singular settings 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. Furthermore, scattering theory for the pair $(H_{m}, H_{om})$ is established and asymptotic expansions of the scattering matrix are derived as the energy parameter tends to the lowest Landau threshold