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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 216, Number 1, Pages 117–132
DOI: https://doi.org/10.4213/tmf10476 (Mi tmf10476) 		 
Inverse scattering problem for the Schrödinger equation with an additional increasing potential on the line

A. Kh. Khanmamedovabcd, D. G. Orudzhevd

a Baku State University, Baku, Republic of Azerbaijan
b Institute of Mathematics and Mechanics, Baku, Republic of Azerbaijan
c Azerbaijan University, Baku, Republic of Azerbaijan
d Baku Engineering University, Baku, Republic of Azerbaijan
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DOI: https://doi.org/10.4213/tmf10476
Abstract: We study the Schrödinger equation with a potential that increases without bound at $+\infty$ and vanishes at $-\infty$. We explore the direct and inverse scattering problems using the transformation operator method. The basic integral equations of the inverse problem are obtained. The basic equations are shown to be uniquely solvable.
Keywords: Schrödinger equation, harmonic oscillator, scattering data, inverse scattering problem, basic integral equations.
Received: 09.02.2023
Revised: 19.03.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 216, Issue 1, Pages 1010–1023
DOI: https://doi.org/10.1134/S0040577923070085
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Kh. Khanmamedov, D. G. Orudzhev, “Inverse scattering problem for the Schrödinger equation with an additional increasing potential on the line”, TMF, 216:1 (2023), 117–132; Theoret. and Math. Phys., 216:1 (2023), 1010–1023
Citation in format AMSBIB
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\by A.~Kh.~Khanmamedov, D.~G.~Orudzhev
\paper Inverse scattering problem for the~Schr\"odinger equation with
an~additional increasing potential on the~line
\jour TMF
\yr 2023
\vol 216
\issue 1
\pages 117--132
\mathnet{http://mi.mathnet.ru/tmf10476}
\crossref{https://doi.org/10.4213/tmf10476}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4619870}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...216.1010K}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 216
\issue 1
\pages 1010--1023
\crossref{https://doi.org/10.1134/S0040577923070085}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85165594449}
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