On solutions of the Schrödinger equation with radiation conditions at infinity: the long-range case
type: Item
instance of: scholarly article
title: On solutions of the Schrödinger equation with radiation conditions at infinity: the long-range case
zbMATH Open document ID: 0939.35050
author: Y. Gâtel
author: Dmitri Yafaev
publication date: 1999-11-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75394
review text: The paper gives a complete description of solutions of the homogeneous Schrödinger equation with a long range potential. It is shown that this solution is asymptotically a sum of incoming and outgoing distorted spherical waves, where the phase must be a suitable chosen approximate solution of the eikonal equation to the potential. So the norm of the incoming and outgoing waves are equal and there exists for any incoming function a outgoing one and a asymptotic solution of the Schrödinger equation, also the roles of incoming and outgoing functions can be interchanged. Finally it is shown that the time dependent scattering matrix can be constructed by this one of the stationary case.
reviewed by: Thoralf Chrobok
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 81U99
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 1355992
zbMATH Keywords: scattering theory
zbMATH Keywords: long-range potentials
zbMATH Keywords: homogeneous Schrödinger equation
zbMATH Keywords: class of solutions
zbMATH Keywords: scattering matrix
MaRDI profile type: Publication
OpenAlex ID: W2334691450
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DOI: 10.5802/AIF.1730
published in: Annales de l’institut Fourier
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description: scientific article; zbMATH DE number 1355992