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 Schr?dinger 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. Received December 11, 2000; accepted in final form June 16, 2001 Published online June 10, 2002