Analytic properties of the scattering matrix of many particle systems
type: Item
instance of: scholarly article
title: Analytic properties of the scattering matrix of many particle systems
zbMATH Open document ID: 0605.47009
DOI: 10.1007/BF01257066
published in: Integral Equations and Operator Theory
publication date: 1986-01-01T00:00:00Z
review text: Analytic properties of the S-matrix are discussed for the many-body problem under the assumptions that the Schrödinger operator is of the form \(-\Delta +\Sigma V_{ij}(x_ i-x_ j)\), \(1\leq i,j\leq N\), and \(V_{ij}\) satisfy a number of technical conditions, in particular \(V_{ij}\) are dilation-analytic and decay exponentially.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 81U10
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 3977731
zbMATH Keywords: S-matrix
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: dilation-analytic
zbMATH Keywords: decay exponentially
author: I. M. Sigal
reviewed by: A. G. Ramm
MaRDI profile type: Publication
cites work: Analytic scattering theory for many-body systems below the smallest three-body threshold
cites work: Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions
cites work: Relatively compact interactions in many particle systems
cites work: Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. IV
cites work: Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators
cites work: A link between scattering resonances and dilation analytic resonances in few body quantum mechanics
cites work: Wave operators and similarity for some non-selfadjoint operators
cites work: Multichannel stationary scattering theory in two-Hilbert space formulation
cites work: Q4185363
cites work: Scattering theory for many-body quantum mechanical systems -rigorous results
cites work: Asymptotic completeness of many-body short-range systems
description: scientific article; zbMATH DE number 3977731