Effective perturbation methods for one-dimensional Schrödinger operators
type: Item
instance of: scholarly article
title: Effective perturbation methods for one-dimensional Schrödinger operators
zbMATH Open document ID: 0921.34076
author: Alexander Kiselev
author: B. Simon
author: Christian Remling
published in: Journal of Differential Equations
publication date: 1999-09-23T00:00:00Z
review text: Starting from the equation \[ -y_0''y=Ey, \] and using the perturbation technique, the authors study properties of solutions and the spectrum of the equation \[ -u''(V_0)u=Eu, \] where \(V\) is small at infinity in some sense. The discrete analogies \[ u(n)(n)(V_0)u(n)=Eu(n) \] are considered.
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 1271350
zbMATH Keywords: Sturm-Liouville operator
zbMATH Keywords: perturbation methods
zbMATH Keywords: spectrum
reviewed by: V. A. Yurko
MaRDI profile type: Publication
OpenAlex ID: W2077397916
cites work: One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types
cites work: Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results
cites work: On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
cites work: Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
cites work: Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
cites work: Modified Prüfer and EFGP transforms and deterministic models with dense point spectrum
cites work: Dense point spectra of Schrödinger and Dirac operators
cites work: On the point spectrum of discrete Schrödinger operator
cites work: Q4002485
cites work: Singular continuous measures in scattering theory
cites work: Value distribution and spectral analysis of differential operators
cites work: The absolute continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
cites work: Q4836262
DOI: 10.1006/JDEQ.1998.3514
Recommended article: Perturbation theory for the one-dimensional Schrödinger scattering problem
Recommended article: Perturbation theory for the one-dimensional Schrodinger scattering problem
Recommended article: Q4781494
Recommended article: Perturbations of a one-dimensional Schrödinger operator with limit- periodic potential
Recommended article: Q3184858
Recommended article: One-dimensional perturbation of operators
Recommended article: A quick perturbative method for Schrödinger equations
Recommended article: Effective approximation for the semiclassical Schrödinger equation
Recommended article: Fourier method for one dimensional Schr\"odinger operators with singular periodic potentials
Recommended article: Q4732950
description: scientific article; zbMATH DE number 1271350