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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 104, Number 2, Pages 356–367 (Mi tmf1344)  

This article is cited in 137 scientific papers (total in 137 papers)

Darboux transformation, factorization, supersymmetry in one-dimensional quantum mechanics

V. G. Bagrova, B. F. Samsonovb

a Tomsk State University
b Institute of High Current Electronics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: We introduce an N-order Darboux transformation operator as a particular case of general transformation operators. It is shown that this operator can always be represented as a product of N first-order Darboux transformation operators. The relationship between this transformation and the factorization method is investigated. Supercharge operators are introduced. They are differential operators of order N. It is shown that these operators and super-Hamiltonian form a superalgebra of order N. For N=2, we have a quadratic superalgebra analogous to the Sklyanin quadratic algebras. The relationship between the transformation introduced and the inverse scattering problem in quantum mechanics is established. An elementary N-parametric potential that has exactly N predetermined discrete spectrum levels is constructed. The paper concludes with some examples of new exactly soluble potentials.
Received: 10.10.1994
English version:
Theoretical and Mathematical Physics, 1995, Volume 104, Issue 2, Pages 1051–1060
DOI: https://doi.org/10.1007/BF02065985
Bibliographic databases:
Language: Russian
Citation: V. G. Bagrov, B. F. Samsonov, “Darboux transformation, factorization, supersymmetry in one-dimensional quantum mechanics”, TMF, 104:2 (1995), 356–367; Theoret. and Math. Phys., 104:2 (1995), 1051–1060
Citation in format AMSBIB
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\by V.~G.~Bagrov, B.~F.~Samsonov
\paper Darboux transformation, factorization, supersymmetry in one-dimensional quantum mechanics
\jour TMF
\yr 1995
\vol 104
\issue 2
\pages 356--367
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1488681}
\zmath{https://zbmath.org/?q=an:0857.34070}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 104
\issue 2
\pages 1051--1060
\crossref{https://doi.org/10.1007/BF02065985}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995UD33400013}
Linking options:
  • https://www.mathnet.ru/eng/tmf1344
  • https://www.mathnet.ru/eng/tmf/v104/i2/p356
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    13. Axel Schulze-Halberg, “Higher-order Darboux transformations and Wronskian representations for Schrödinger equations with quadratically energy-dependent potentials”, Journal of Mathematical Physics, 61:2 (2020)  crossref
    14. Axel Schulze-Halberg, “Generalized Schrödinger equations with quadratical energy-dependence in the potential: Darboux transformations and application to the Heun class”, Journal of Mathematical Physics, 61:8 (2020)  crossref
    15. S Cruz y Cruz, R Razo, O Rosas-Ortiz, K Zelaya, “Coherent states for exactly solvable time-dependent oscillators generated by Darboux transformations”, Phys. Scr., 95:4 (2020), 044009  crossref
    16. Ekaterina Shemyakova, “Classification of Darboux transformations for operators of the form ∂x∂y+a∂x+b∂y+c”, Illinois J. Math., 64:1 (2020)  crossref
    17. Kyle R. Bryenton, Nasser Saad, “Exactly solvable Schrödinger eigenvalue problems for new anharmonic potentials with variable bumps and depths”, Eur. Phys. J. Plus, 135:4 (2020)  crossref
    18. Axel Schulze-Halberg, Matthew Paskash, “Wronskian representation of second-order Darboux transformations for Schrödinger equations with quadratically energy-dependent potentials”, Phys. Scr., 95:1 (2020), 015001  crossref
    19. S. V. Smirnov, “Factorization of Darboux–Laplace transformations for discrete hyperbolic operators”, Theoret. and Math. Phys., 199:2 (2019), 621–636  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    20. David J. Fernández C., Integrability, Supersymmetry and Coherent States, 2019, 37  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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