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Energy dependent boundary conditions and few-body scattering problem

Kurasov, Pavel LU (1997) In Reviews in Mathematical Physics 9(7). p.853-906
Abstract
An exactly solvable problem with energy dependent interaction is investigated in the present paper. The selfadjoint model operator describes the scattering problem for three one-dimensional particles. It is shown that this problem is equivalent to the diffraction problem in the sector with energy dependent boundary conditions. The problem is solved with the help of the Sommerfeld-Maluzhinetz representation, which transforms the partial differential equation for the eigenfunctions to a functional equation on the integral densities. The solution of the functional equation can be constructed explicitly in the case of identical particles. The three-body scattering matrix describing rearrangement and excitation processes is represented in terms... (More)
An exactly solvable problem with energy dependent interaction is investigated in the present paper. The selfadjoint model operator describes the scattering problem for three one-dimensional particles. It is shown that this problem is equivalent to the diffraction problem in the sector with energy dependent boundary conditions. The problem is solved with the help of the Sommerfeld-Maluzhinetz representation, which transforms the partial differential equation for the eigenfunctions to a functional equation on the integral densities. The solution of the functional equation can be constructed explicitly in the case of identical particles. The three-body scattering matrix describing rearrangement and excitation processes is represented in terms of analytic functions. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
INVERSE SCATTERING, INTERNAL STRUCTURE, OPERATORS, HAMILTONIANS, LINE
in
Reviews in Mathematical Physics
volume
9
issue
7
pages
853 - 906
publisher
World Scientific
ISSN
0129-055X
DOI
10.1142/S0129055X97000300
language
English
LU publication?
yes
id
03f798db-3308-4734-a174-aa86b8f81f56 (old id 758076)
alternative location
http://s0129055x97000300.pdf/
date added to LUP
2008-09-01 16:19:16
date last changed
2016-04-16 04:29:12
@article{03f798db-3308-4734-a174-aa86b8f81f56,
  abstract     = {An exactly solvable problem with energy dependent interaction is investigated in the present paper. The selfadjoint model operator describes the scattering problem for three one-dimensional particles. It is shown that this problem is equivalent to the diffraction problem in the sector with energy dependent boundary conditions. The problem is solved with the help of the Sommerfeld-Maluzhinetz representation, which transforms the partial differential equation for the eigenfunctions to a functional equation on the integral densities. The solution of the functional equation can be constructed explicitly in the case of identical particles. The three-body scattering matrix describing rearrangement and excitation processes is represented in terms of analytic functions.},
  author       = {Kurasov, Pavel},
  issn         = {0129-055X},
  keyword      = {INVERSE SCATTERING,INTERNAL STRUCTURE,OPERATORS,HAMILTONIANS,LINE},
  language     = {eng},
  number       = {7},
  pages        = {853--906},
  publisher    = {World Scientific},
  series       = {Reviews in Mathematical Physics},
  title        = {Energy dependent boundary conditions and few-body scattering problem},
  url          = {http://dx.doi.org/10.1142/S0129055X97000300},
  volume       = {9},
  year         = {1997},
}