Scattering matrices with finite phase shift and the inverse scattering problem
(1996) In Inverse Problems 12(3). p.295307 Abstract
 The inverse scattering problem for the Schrodinger operator on the halfaxis 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 longrange oscillating tails at infinity. The solution of the problem is constructed with the help of the GelfandLevitanMarchenko 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 halfaxis 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 longrange oscillating tails at infinity. The solution of the problem is constructed with the help of the GelfandLevitanMarchenko 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
 02665611
 DOI
 10.1088/02665611/12/3/009
 language
 English
 LU publication?
 yes
 id
 33aa896df8ba44718264da5b9e2fd8e8 (old id 758071)
 alternative location
 http://www.iop.org/EJ/article/02665611/12/3/009/ip6308.pdf?requestid=7153b802a4f4426eb47bb47a9aa45c11
 date added to LUP
 20160401 12:11:50
 date last changed
 20220127 00:16:17
@article{33aa896df8ba44718264da5b9e2fd8e8, abstract = {{The inverse scattering problem for the Schrodinger operator on the halfaxis 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 longrange oscillating tails at infinity. The solution of the problem is constructed with the help of the GelfandLevitanMarchenko 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 = {{02665611}}, keywords = {{REFLECTION COEFFICIENT; POTENTIALS}}, language = {{eng}}, number = {{3}}, pages = {{295307}}, publisher = {{IOP Publishing}}, series = {{Inverse Problems}}, title = {{Scattering matrices with finite phase shift and the inverse scattering problem}}, url = {{http://dx.doi.org/10.1088/02665611/12/3/009}}, doi = {{10.1088/02665611/12/3/009}}, volume = {{12}}, year = {{1996}}, }