München 1997 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 8: Endliche Quantensysteme

MP 8.6: Fachvortrag

Donnerstag, 20. März 1997, 16:00–16:20, HS 110

Geometrical Approach to Inverse Scattering for the Schrödinger Equation with Magnetic and Electric Potentials — •Silke Arians — Institut für Reine u. Angewandte Mathematik, RWTH Aachen, D-52056 Aachen

We consider the Hamiltonian H=(p−A(x))²/(2m)+V(x) of a quantum particle in a magnetic field B=rotA and a potential V in space dimensions ν≥ 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.