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On the asymptotics of scattering phases for the Schroedinger equation

Technical Report:

Abstract

Scattering phase are defined in terms of asymptotics of solutions of the Schroedinger equation behaving as standing waves at infinity. The scattering phases are connected in a simple way with the eigenvalues of the unitary operator {Sigma} = S{Iota} where S is the scattering matrix and {Iota} is the reflection operator. The eigenvalues of {Sigma} can accumulate only at the points 1 and -1. It is shown that the leading terms of their asymptotics are determined only by the asymptotics of the even part of the potential at infinity. Explicit expressions for these terms are obtained. (au).
Authors:
Yafaev, D R [1] 
  1. Leningrad Branch of Mathematical Institute (USSR)
Publication Date:
Dec 22, 1989
Product Type:
Technical Report
Report Number:
LITH-MAT-R-89-38
Reference Number:
SCA: 661100; PA: AIX-23:012827; SN: 92000638727
Resource Relation:
Other Information: PBD: 22 Dec 1989
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; SCHROEDINGER EQUATION; SCATTERING AMPLITUDES; ASYMPTOTIC SOLUTIONS; EIGENVALUES; STANDING WAVES; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10111531
Research Organizations:
Linkoeping Univ. (Sweden). Dept. of Mathematics
Country of Origin:
Sweden
Language:
English
Other Identifying Numbers:
Other: ON: DE92614129; TRN: SE9100273012827
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
SWDN
Size:
18 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Yafaev, D R. On the asymptotics of scattering phases for the Schroedinger equation. Sweden: N. p., 1989. Web.
Yafaev, D R. On the asymptotics of scattering phases for the Schroedinger equation. Sweden.
Yafaev, D R. 1989. "On the asymptotics of scattering phases for the Schroedinger equation." Sweden.
@misc{etde_10111531,
title = {On the asymptotics of scattering phases for the Schroedinger equation}
author = {Yafaev, D R}
abstractNote = {Scattering phase are defined in terms of asymptotics of solutions of the Schroedinger equation behaving as standing waves at infinity. The scattering phases are connected in a simple way with the eigenvalues of the unitary operator {Sigma} = S{Iota} where S is the scattering matrix and {Iota} is the reflection operator. The eigenvalues of {Sigma} can accumulate only at the points 1 and -1. It is shown that the leading terms of their asymptotics are determined only by the asymptotics of the even part of the potential at infinity. Explicit expressions for these terms are obtained. (au).}
place = {Sweden}
year = {1989}
month = {Dec}
}