Abstract
The scattering problem related to the Schrodinger operator with an external constant homogeneous magnetic field is considered. The behaviour of the corresponding S-matrix and resolvent operator near the Landau thresholds is studied. The large-energy asymptotics of the resolvent operator are evaluated. A Levinson-type formula is obtained. It relates the number of bound states to the determinant of the scattering matrix in the scattering threshold.
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