Inverse scattering problem for the Schrödinger equation with an additional increasing potential on the line

We study the Schrödinger equation with a potential that increases without bound at and vanishes at . 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 u...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2023-07, Vol.216 (1), p.1010-1023
Main Authors: Khanmamedov, A. Kh, Orudzhev, D. G.
Format: Article
Language:English
Subjects:
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Applications of Mathematics
Integral equations
Inverse problems
Inverse scattering
Mathematical analysis
Mathematical and Computational Physics
Physics
Physics and Astronomy
Schrodinger equation
Theoretical
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Summary:We study the Schrödinger equation with a potential that increases without bound at and vanishes at . 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.
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577923070085