The resonance selection principle for the three-dimensional Schrödinger operator
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 \(| x| \to 0\).
scientific article; zbMATH DE number 3859631