Scattering matrices with finite phase shift and the inverse scattering problem
(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:
https://lup.lub.lu.se/record/758071
- author
- Kurasov, Pavel LU
- organization
- publishing date
- 1996
- 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
- 2016-04-01 12:11:50
- date last changed
- 2022-01-27 00:16:17
@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}},
keywords = {{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}},
doi = {{10.1088/0266-5611/12/3/009}},
volume = {{12}},
year = {{1996}},
}