Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

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...

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Veröffentlicht in:Theoretical and mathematical physics 2018-04, Vol.195 (1), p.538-547
Hauptverfasser: Guseinov, I. M., Khanmamedov, A. Kh, Mamedova, A. F.
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Integral equations
Inverse problems
Inverse scattering
Mathematical analysis
Mathematical and Computational Physics
Operators (mathematics)
Physics
Physics and Astronomy
Schrodinger equation
Theoretical
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Zusammenfassung: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.
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577918040050