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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 195, Number 1, Pages 54–63
DOI: https://doi.org/10.4213/tmf9423 (Mi tmf9423) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Inverse scattering problem for the Schrödinger equation with an additional quadratic potential on the entire axis

I. M. Guseinovabc, A. Kh. Khanmamedovabc, A. F. Mamedovab

a Baku State University, Baku, Azerbaijan
b Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
c Azerbaijan University, Baku, Azerbaijan
Full-text PDF (419 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf9423
Abstract: 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.
Keywords: Schrödinger equation, oscillator, reflection coefficient, inverse scattering problem, basic equation.
Received: 20.06.2017
Revised: 13.08.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 195, Issue 1, Pages 538–547
DOI: https://doi.org/10.1134/S0040577918040050
Bibliographic databases:
Document Type: Article
MSC: 34A55, 34B24, 34L05
Language: Russian
Citation: I. M. Guseinov, A. Kh. Khanmamedov, A. F. Mamedova, “Inverse scattering problem for the Schrödinger equation with an additional quadratic potential on the entire axis”, TMF, 195:1 (2018), 54–63; Theoret. and Math. Phys., 195:1 (2018), 538–547
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9423
  • https://doi.org/10.4213/tmf9423
  • https://www.mathnet.ru/eng/tmf/v195/i1/p54
    • This publication is cited in the following 7 articles:
    1. A. Kh. Khanmamedov, D. G. Orudzhev, “Inverse scattering problem for the Schrödinger equation with an additional increasing potential on the line”, Theoret. and Math. Phys., 216:1 (2023), 1010–1023  mathnet  crossref  crossref  mathscinet  adsnasa
    2. A. K. Khanmamedov, N. F. Gafarova, “Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition”, J. Inverse Ill-Posed Probl., 29:5 (2021), 675–688  crossref  mathscinet  isi
    3. A. Kh. Khanmamedov, A. F. Mamedova, “A note on the Schrödinger operator with exponential potential”, Proc. Inst. Math. Mech., 47:1 (2021), 138–142  mathscinet  isi
    4. A. Kh. Khanmamedov, M. G. Makhmudova, “On the transformation operator for the Schrödinger equation with an additional linear potential”, Funct. Anal. Appl., 54:1 (2020), 73–76  mathnet  crossref  crossref  mathscinet  isi  elib
    5. A. Kh. Khanmamedov, M. G. Makhmudova, “Inverse spectral problem for the Schrödinger equation with an additional linear potential”, Theoret. and Math. Phys., 202:1 (2020), 58–71  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. A. R. Latifova, A. Kh. Khanmamedov, “Inverse spectral problem for the one-dimensional stark operator on the semiaxis”, Ukr. Math. J., 72:4 (2020), 568–584  crossref  mathscinet  zmath  isi
    7. A. R. Latifova, A. Kh. Khanmamedov, “Obratnaya spektralnaya zadacha dlya odnomernogo operatora Shtarka na poluosi”, Ukr. Mat. Zhurn., 72:4 (2020), 494  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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