Corrections to the classical behavior of the number of bound states of Schrödinger operators
type: Item
instance of: scholarly article
title: Corrections to the classical behavior of the number of bound states of Schrödinger operators
zbMATH Open document ID: 0646.35019
DOI: 10.1016/0003-4916(88)90248-5
published in: Annals of Physics
publication date: 1988-01-01T00:00:00Z
review text: Let us denote by \(N_ E\) the number of bound states of the Schrödinger operator \(H=-\Delta -c/(1+| x|^ 2)+V_ 0\) below -E. \(V_ 0\) is a potential decaying at infinity sufficiently fast. We prove that, for dimension \(d=1\), \(\lim_{E\downarrow 0}(N_ E/| \ln E|)=(1/\pi)\sqrt{c-1/4}\) and for \(d=3\), \(\lim_{E\downarrow 0}(N_ E/| \ln E|)=\sum^{[\sqrt{c}-]}_{l=0}(2l+1)\sqrt{c-(l+)^ 2}\).
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 4054147
zbMATH Keywords: bound states
zbMATH Keywords: Schrödinger operator
author: Werner Kirsch
author: B. Simon
reviewed by: Werner Kirsch
MaRDI profile type: Publication
full work available at URL: 0003-4916(88)90248-5
OpenAlex ID: W2047935756
cites work: Spherical harmonics
cites work: Q4066072
cites work: Q4185363
description: scientific article; zbMATH DE number 4054147