Inverse scattering problem for one-dimensional Schrödinger operators related to the general Stark effect
type: Item
instance of: scholarly article
title: Inverse scattering problem for one-dimensional Schrödinger operators related to the general Stark effect
zbMATH Open document ID: 0699.35200
DOI: 10.1007/BF02009745
author: N. E. Zubov
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1989-01-01T00:00:00Z
review text: This paper discusses the inverse scattering problem for the one- dimensional Schrödinger operator on (-\(\infty,\infty)\), \(H=H_ 0+q(x)\), \(H_ 0=-d^ 2/dx^ 2+Q(x)\) with \(q\in C^{\infty}_ 0({\mathbb{R}})\), \(Q\in C^ 1({\mathbb{R}})\). It is proved that q(x) can be determined by the scattering data. The method used in this work provides a general framework which can be applied both to the Stark effect operator \((Q(x)=x)\) and to the zero potential operator \((Q(x)=0)\).
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 81U99
zbMATH DE Number: 4146672
zbMATH Keywords: inverse problem
zbMATH Keywords: inverse scattering problem
zbMATH Keywords: one-dimensional Schrödinger operator
zbMATH Keywords: Stark effect
reviewed by: Pierre Hillion
MaRDI profile type: Publication
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cites work: Variational Principles for Scattering Processes. I
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cites work: Spectral and scattering theory of Schrödinger operators related to the Stark effect
description: scientific article; zbMATH DE number 4146672