Arians S.
Geometric Approach to Inverse Scattering for the Schroedinger Equation
with Magnetic and Electric Potentials
(38K, LaTeX 2.09)

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.
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