Analog of Levinson's formula for a Schrödinger operator with long-range potential
type: Item
instance of: scholarly article
title: Analog of Levinson's formula for a Schrödinger operator with long-range potential
zbMATH Open document ID: 0625.35021
DOI: 10.1007/BF01035543
published in: Theoretical and Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: Trace formulas of order zero are obtained for a radial Schrödinger operator with long-range potential V(x) that decreases as \(x\to \infty\) as the power \(x^{-\alpha}\) with \(1\leq \alpha \leq 2\). These formulas relate the increment of the phase shift in the continuum to the characteristics of the discrete spectrum and generalize Levinson's theorem to the case of slowly decreasing potentials.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4015266
zbMATH Keywords: Trace formulas
zbMATH Keywords: radial Schrödinger operator
zbMATH Keywords: long-range potential
zbMATH Keywords: phase shift
zbMATH Keywords: discrete spectrum
zbMATH Keywords: Levinson's theorem
zbMATH Keywords: slowly decreasing potentials
author: A. A. Kvitsinskiĭ
MaRDI profile type: Publication
cites work: Causality and dispersion relations for fixed momentum transfer
cites work: The low energy scattering for slowly decreasing potentials
cites work: On a Factor Automorphism of a Normal Dynamical System
cites work: Q5558293
full work available at URL: https://doi.org/10.1007/bf01035543
OpenAlex ID: W4241808102
description: scientific article; zbMATH DE number 4015266