Abstract
We consider the Hamiltonian of one quantum particle in a homogeneous magnetic field and a scalar potential in three space dimensions. For a given magnetic field the high velocity limit of the scattering operator uniquely determines the scalar potential if it is of short range. If, in addition, long-range potentials are present, some knowledge of (the far out tail of) the long-range part is needed to define a modified Dollard wave operator and a scattering operator. Again its high velocity limit uniquely determines the total scalar potential for a given magnetic field. We generalize our results to a system of two interacting quantum particles with opposite electric charges.
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