The resonance selection principle for the three-dimensional Schrödinger operator
type: Item
instance of: scholarly article
title: The resonance selection principle for the three-dimensional Schrödinger operator
zbMATH Open document ID: 0541.35064
author: M. A. Shubova
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: 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 \(| x| \to 0\).
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 3859631
zbMATH Keywords: Resonances
zbMATH Keywords: Schrödinger operator
reviewed by: Dmitri Yafaev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3859631