Construction of a two-dimensional Schrödinger operator with given scattering amplitude at fixed energy
type: Item
instance of: scholarly article
title: Construction of a two-dimensional Schrödinger operator with given scattering amplitude at fixed energy
zbMATH Open document ID: 0615.35023
DOI: 10.1007/BF01017767
published in: Theoretical and Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: The inverse scattering problem for the two-dimensional Schrödinger operator \(H=-\Delta +V(x,y)\) is considered. It is shown that the classical necessary properties of the scattering amplitude (duality and unitarity) are sufficient conditions for the existence of a decreasing potential with given scattering amplitude at fixed energy, if the \(L^ 2\) norm of the amplitude is small.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 81U99
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 3996215
zbMATH Keywords: inverse scattering problem
zbMATH Keywords: two-dimensional Schrödinger operator
zbMATH Keywords: scattering amplitude
zbMATH Keywords: duality
zbMATH Keywords: unitarity
zbMATH Keywords: decreasing potential
zbMATH Keywords: fixed energy
author: R. G. Novikov
reviewed by: B. Konopelchenko
MaRDI profile type: Publication
cites work: Q4137669
cites work: Q3695595
cites work: Q5569399
full work available at URL: https://doi.org/10.1007/bf01017767
OpenAlex ID: W2039549511
description: scientific article; zbMATH DE number 3996215