Resonances for Schrodinger operators with compactly supported potentials

Abstract

We describe the generic behavior of the resonance counting function for a Schrödinger operator with a bounded, compactly-supported real or complex valued potential in $d\ge 1$ dimensions. This note contains a sketch of the proof of our main results \cite{ch-hi1,ch-hi2} that generically the order of growth of the resonance counting function is the maximal value $d$ in the odd dimensional case, and that it is the maximal value $d$ on each nonphysical sheet of the logarithmic Riemann surface in the even dimensional case. We include a review of previous results concerning the resonance counting functions for Schrödinger operators with compactly-supported potentials.

19 pages

References in corpus (1)

• Maximal order of growth for the resonance counting functions for generic potentials in even dimensions