On the Inverse Scattering Problem for the SchrödingeEquation with Increasing Potential

Khanmamedov A. K., MƏMMƏDOVA A.

Azerbaijan Journal of Mathematics, vol.15, no.2, pp.105-112, 2025 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.59849/2218-6816.2025.2.105
  • Journal Name: Azerbaijan Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.105-112
  • Keywords: Airy function, inverse scattering problem, Macdonald functiongrowing potential, main integral equations, Schrödinger equation
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

The one-dimensional Schrödinger equation on the entire axis is considered, the potential of which at the left end grows as a quadratic function, and at the right end as a linear function. The inverse scattering problem is studied by the method of transformation operators. The main integral equations of the Marchenko type are obtained, allowing the inverse problem to be solved.