96-380 Arians S.

Geometric Approach to Inverse Scattering for the Schroedinger Equation with Magnetic and Electric Potentials (38K, LaTeX 2.09) Aug 21, 96

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Abstract. 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 greater or equal 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. This paper is also available by anonymous ftp from work1.iram.rwth-aachen.de (134.130.161.65) in the directory /pub/papers/arians as a LaTeX 2.09 tex, dvi or ps file ar-96-1.*.

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