On the Inverse Scattering Problem for the One-Dimensional Schrödinger Equation with Increasing Potential
| Autor: | Ag. Kh. Khanmamedov, I. M. Guseinov |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Scattering
General Mathematics 010102 general mathematics Mathematical analysis Inverse problem 01 natural sciences Integral equation Schrödinger equation 010101 applied mathematics symbols.namesake Transformation (function) Inverse scattering problem symbols 0101 mathematics Algebra over a field Mathematics |
| Zdroj: | Ukrainian Mathematical Journal. 70:1604-1618 |
| ISSN: | 1573-9376 0041-5995 |
| DOI: | 10.1007/s11253-019-01593-z |
| Popis: | We consider a one-dimensional Schrodinger equation on the entire axis whose potential rapidly decreases on the left-hand side and infinitely increases on the right-hand side. By the method of transformation operators, we study the inverse scattering problem. We establish conditions for the scattering data under which the inverse problem is solvable. The main Marchenko-type integral equations are investigated and their unique solvability is established. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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