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TMF, 2018, Volume 195, Number 1, Pages 54–63 (Mi tmf9423)  

Inverse scattering problem for the Schrödinger equation with an additional quadratic potential on the entire axis

I. M. Guseinovabc, A. Kh. Khanmamedovabc, A. F. Mamedovab

a Baku State University, Baku, Azerbaijan
b Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
c Azerbaijan University, Baku, Azerbaijan

Abstract: We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Keywords: Schrödinger equation, oscillator, reflection coefficient, inverse scattering problem, basic equation

DOI: https://doi.org/10.4213/tmf9423

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English version:
Theoretical and Mathematical Physics, 2018, 195:1, 538–547

Bibliographic databases:

Document Type: Article
MSC: 34A55, 34B24, 34L05
Received: 20.06.2017
Revised: 13.08.2017

Citation: I. M. Guseinov, A. Kh. Khanmamedov, A. F. Mamedova, “Inverse scattering problem for the Schrödinger equation with an additional quadratic potential on the entire axis”, TMF, 195:1 (2018), 54–63; Theoret. and Math. Phys., 195:1 (2018), 538–547

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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