Geometric approach to inverse scattering for the Schrodinger equation with magnetic and electric potentials

We consider the Hamiltonian H=(p-A(x))(2)/(2m)+V(x) of a quantum particle in a magnetic field B=rot A and a potential V in space dimensions nu greater than or equal to 2. If V is of short. range, then the high-velocity limit of the scattering operator uniquely determines the magnetic field B and the potential V. If, in addition, long-range potentials V-l are present, some knowledge of (the far out tail of) V-l is needed to define a modified Dollard wave operator and a scattering operator S-D. Again its high-velocity limit uniquely determines B and V=V-S+V-l. Moreover, we give explicit error bounds which are inverse proportional to the velocity. (C) 1997 American Institute of Physics.