Scattering theory for one-dimensional systems with \(\int dx\,V(x)=0\)
type: Item
instance of: scholarly article
title: Scattering theory for one-dimensional systems with \(\int dx\,V(x)=0\)
zbMATH Open document ID: 0617.35105
DOI: 10.1016/0022-247X(87)90281-2
author: D. Bollé
author: Martin Klaus
author: Fritz Gesztesy
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: Low-energy scattering for Schrödinger operators of the type \(H=-\Delta \dot +V\) in \(L^ 2({\mathbb{R}})\) with \(\int_{{\mathbb{R}}}dx V(x)=0\) is considered. The possibility of zero-energy eigenstates of H is taken into account explicitly. In particular, a Laurent expansion for the transition operator and recursion relations for its coefficients are provided and the leading behaviour of the scattering operator is given in all possible cases.
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 4000573
zbMATH Keywords: Low-energy scattering
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: zero-energy eigenstates
zbMATH Keywords: Laurent expansion
zbMATH Keywords: transition operator
zbMATH Keywords: scattering operator
MaRDI profile type: Publication
cites work: Q3994511
cites work: Q3683036
cites work: The bound state of weakly coupled Schrödinger operators in one and two dimensions
full work available at URL: 0022-247x(87)90281-2
OpenAlex ID: W1971266606
description: scientific article; zbMATH DE number 4000573