This article is cited in 1 paper

Inverse spectral problem for the Schrödinger equation with an additional linear potential

A. Kh. Khanmamedov^abc, M. G. Makhmudova<sup>b

a</sup> Baku State University, Baku, Azerbaijan
^b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
^c Azerbaijan University, Baku, Azerbaijan

Abstract: We consider the one-dimensional Schrödinger equation with an additional linear potential on the whole axis and construct a transformation operator with a condition at $-\infty$. We obtain the fundamental integral Gelfand–Levitan equation on the half-axis $(-\infty,x)$ and prove the unique solvability of this fundamental equation.

Keywords: Schrödinger equation, additional linear potential, Airy function, transformation operator, Gelfand–Levitan equation, inverse scattering problem.

Received: 26.05.2019
Revised: 30.08.2019

DOI: 10.4213/tmf9755

 English version: Theoretical and Mathematical Physics, 2020, 202:1, 58–71

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