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Scattering matrices with finite phase shift and the inverse scattering problem

Kurasov, Pavel LU (1996) In Inverse Problems 12(3). p.295-307
Abstract
The inverse scattering problem for the Schrodinger operator on the half-axis is studied. It is shown that this problem can be solved for the scattering matrices with arbitrary finite phase shift on the real axis if one admits potentials with long-range oscillating tails at infinity. The solution of the problem is constructed with the help of the Gelfand-Levitan-Marchenko procedure. The inverse problem has no unique solution for the standard set of scattering data which includes the scattering matrix, energies of the bound states and corresponding normalizing constants. This fact is related to zeros of the spectral density on the real axis. It is proven that the inverse problem has a unique solution in the defined class of potentials if the... (More)
The inverse scattering problem for the Schrodinger operator on the half-axis is studied. It is shown that this problem can be solved for the scattering matrices with arbitrary finite phase shift on the real axis if one admits potentials with long-range oscillating tails at infinity. The solution of the problem is constructed with the help of the Gelfand-Levitan-Marchenko procedure. The inverse problem has no unique solution for the standard set of scattering data which includes the scattering matrix, energies of the bound states and corresponding normalizing constants. This fact is related to zeros of the spectral density on the real axis. It is proven that the inverse problem has a unique solution in the defined class of potentials if the zeros of the spectral density are added to the set of scattering data. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
REFLECTION COEFFICIENT, POTENTIALS
in
Inverse Problems
volume
12
issue
3
pages
295 - 307
publisher
IOP Publishing
external identifiers
  • scopus:0040483942
ISSN
0266-5611
DOI
10.1088/0266-5611/12/3/009
language
English
LU publication?
yes
id
33aa896d-f8ba-4471-8264-da5b9e2fd8e8 (old id 758071)
alternative location
http://www.iop.org/EJ/article/0266-5611/12/3/009/ip6308.pdf?request-id=7153b802-a4f4-426e-b47b-b47a9aa45c11
date added to LUP
2008-09-01 16:14:16
date last changed
2017-01-01 04:55:43
@article{33aa896d-f8ba-4471-8264-da5b9e2fd8e8,
  abstract     = {The inverse scattering problem for the Schrodinger operator on the half-axis is studied. It is shown that this problem can be solved for the scattering matrices with arbitrary finite phase shift on the real axis if one admits potentials with long-range oscillating tails at infinity. The solution of the problem is constructed with the help of the Gelfand-Levitan-Marchenko procedure. The inverse problem has no unique solution for the standard set of scattering data which includes the scattering matrix, energies of the bound states and corresponding normalizing constants. This fact is related to zeros of the spectral density on the real axis. It is proven that the inverse problem has a unique solution in the defined class of potentials if the zeros of the spectral density are added to the set of scattering data.},
  author       = {Kurasov, Pavel},
  issn         = {0266-5611},
  keyword      = {REFLECTION COEFFICIENT,POTENTIALS},
  language     = {eng},
  number       = {3},
  pages        = {295--307},
  publisher    = {IOP Publishing},
  series       = {Inverse Problems},
  title        = {Scattering matrices with finite phase shift and the inverse scattering problem},
  url          = {http://dx.doi.org/10.1088/0266-5611/12/3/009},
  volume       = {12},
  year         = {1996},
}