Resonances for Schrödinger operators with compactly supported potentials | Zendy

T. J. Christiansen | Zendy; Peter D. Hislop | Zendy

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Resonances for Schrödinger operators with compactly supported potentials

Author(s) -

T. J. Christiansen,

Peter D. Hislop

Publication year - 2010

Publication title -

journées équations aux dérivées partielles

Language(s) - English

Resource type - Journals

eISSN - 2118-9366

pISSN - 0752-0360

DOI - 10.5802/jedp.47

Subject(s) - bounded function , logarithm , resonance (particle physics) , operator (biology) , mathematics , schrödinger's cat , function (biology) , order (exchange) , sketch , riemann hypothesis , pure mathematics , mathematical analysis , physics , quantum mechanics , algorithm , chemistry , biochemistry , finance , repressor , evolutionary biology , biology , transcription factor , economics , gene

We describe the generic behavior of the resonance counting function for a Schr\"odinger operator with a bounded, compactly-supported real or complex valued potential in $d \geq 1$ 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 Schr\"odinger operators with compactly-supported potentials.

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