The resonance selection principle for the three-dimensional Schrödinger operator (Q794207)
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scientific article; zbMATH DE number 3859631
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The resonance selection principle for the three-dimensional Schrödinger operator |
scientific article; zbMATH DE number 3859631 |
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The resonance selection principle for the three-dimensional Schrödinger operator (English)
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1984
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Resonances of the Schrödinger operator \(-\Delta +q(x)\) are investigated. The non-radial function q(x) is supposed to have compact support. The purpose of the paper is to describe resonances in terms of solutions of the differential equation \((1)\quad(-\Delta +q(x)-k^ 2)u(x,k)=0.\) It is proven that k is a resonance iff the so-called singular solution of (1) satisfies a certain condition as \(| x| \to 0\).
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Resonances
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Schrödinger operator
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