99-225 Marius Mantoiu, Serge Richard

Absence of Singular Spectrum for Schrodinger Operators with Anisotropic Potentials and Magnetic Fields (491K, LaTeX) Jun 10, 99

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Abstract. We study magnetic Schrodinger operators of the form H=(P-a)^2+V in L^2(Y+Z), with dim(Y)=m>1. We get a limiting absorption principle and the absence of singular spectrum under rather mild and especially anisotropic hypothesis. The magnetic field B and the potential V will be connected by some Y-conditions, but in the Z-variable there will be almost no constraints. If m=2 and dim(Z)=0, our results contrast with the known fact that P^2+V has always bound states if V is negative.

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