Resonances for Schrödinger operators with compactly supported potentials

Christiansen, T. J.; Hislop, P. D.

Journées équations aux dérivées partielles (2008), article no. 3, 18 p.

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 [5, 6] 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.

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