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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 202, Number 1, Pages 66–80
DOI: https://doi.org/10.4213/tmf9755 (Mi tmf9755) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

A. Kh. Khanmamedovabc, M. G. Makhmudovab

a Baku State University, Baku, Azerbaijan
b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
c Azerbaijan University, Baku, Azerbaijan
Full-text PDF (461 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf9755
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 −∞. We obtain the fundamental integral Gelfand–Levitan equation on the half-axis (−∞,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
English version:
Theoretical and Mathematical Physics, 2020, Volume 202, Issue 1, Pages 58–71
DOI: https://doi.org/10.1134/S0040577920010067
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Kh. Khanmamedov, M. G. Makhmudova, “Inverse spectral problem for the Schrödinger equation with an additional linear potential”, TMF, 202:1 (2020), 66–80; Theoret. and Math. Phys., 202:1 (2020), 58–71
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9755
  • https://www.mathnet.ru/eng/tmf/v202/i1/p66
    • This publication is cited in the following 1 articles:
    1. J. H. Toloza, A. Uribe, “The Dirichlet problem for perturbed Stark operators in the half-line”, Anal. Math. Phys., 13:1 (2023), 8  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Full-text PDF :91
    References:43
    First page:14
     
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