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TMF, 2015, Volume 183, Number 2, Pages 312–328 (Mi tmf8784)  

This article is cited in 6 scientific papers (total in 6 papers)

Generation of exactly solvable potentials of the $D$-dimensional position-dependent mass Schrödinger equation using the transformation method

H. Rajbongshia, N. N. Singhb

a Nalbari College, Nalbari, Assam, India
b Gauhati University, Guwahati, Assam, India

Abstract: We apply the extended transformation method to the constant-mass radial Schrödinger equation satisfied by a radially symmetric central potential in order to obtain exactly solvable quantum systems with a position-dependent mass in a space of arbitrary dimension in the nonrelativistic limit. The method consists of a coordinate transformation, a subsequent functional transformation, and a set of ansatzes for the mass function leading to the appearance of exactly solvable quantum systems with position-dependent masses. We also show that the Zhu–Kroemer ordering for the fitting parameter values is natural for systems with a radially symmetric mass function and a central potential. As an example, we apply the method to the Manning–Rosen potential and to the Morse potential with different choices of the mass functions. We also indicate an application of the method to the Hulthen potential.

Keywords: position-dependent mass, exact analytic solution, Manning–Rosen potential, Morse potential, extended transformation

DOI: https://doi.org/10.4213/tmf8784

Full text: PDF file (488 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 183:2, 715–729

Bibliographic databases:

PACS: 03.65.-w, 03.65.Ge, 03.65.Fd
Received: 27.08.2014

Citation: H. Rajbongshi, N. N. Singh, “Generation of exactly solvable potentials of the $D$-dimensional position-dependent mass Schrödinger equation using the transformation method”, TMF, 183:2 (2015), 312–328; Theoret. and Math. Phys., 183:2 (2015), 715–729

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. H. Rajbongshi, “Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in $D$-dimensional space”, Theoret. and Math. Phys., 184:1 (2015), 996–1010  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. S. Miraboutalebi, “Solutions of Morse potential with position-dependent mass by Laplace transform”, J. Theor. Appl. Phys., 10:4 (2016), 323–328  crossref  isi  elib  scopus
    3. M. V. Ioffe, E. V. Kolevatova, D. N. Nishnianidze, “SUSY method for the three-dimensional Schrödinger equation with effective mass”, Phys. Lett. A, 380:41 (2016), 3349–3354  crossref  mathscinet  zmath  isi  elib  scopus
    4. R. Bravo, M. S. Plyushchay, “Position-dependent mass, finite-gap systems, and supersymmetry”, Phys. Rev. D, 93:10 (2016), 105023  crossref  mathscinet  isi  elib  scopus
    5. B. Rath, P. Mallick, J. Akande, P. Mohapatra, D. K. K. Adjai, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia, R. R. Sahoo, “A general type of Lienard second order differential equation: classical and quantum mechanical study”, Proc. Indian Natl. Sci. Acad., 83:4 (2017), 935–940  crossref  mathscinet  isi
    6. H. Rajbongshi, “Exact analytic solution of position-dependent mass Schrödinger equation”, Indian J. Phys., 92:3 (2018), 357–367  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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