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Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in D-dimensional space

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Abstract

We propose a transformation method using properties of classical orthogonal polynomials to construct exactly solvable potentials that provide bound-state solutions of Schrödinger equations with a position-dependent mass in D-dimensional space. The important feature of the method is that it favors the Zhu—Kroemer ordering of ambiguities for a radially symmetric mass function and potential. This is illustrated using hypergeometric polynomials and the associated Legendre polynomials.

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Authors and Affiliations

  1. Physics Department, Nalbari College, Nalbari, Assam, India

    H. Rajbongshi

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  1. H. Rajbongshi
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Correspondence to H. Rajbongshi.

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 1, pp. 117–133, July, 2015.

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Rajbongshi, H. Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in D-dimensional space. Theor Math Phys 184, 996–1010 (2015). https://doi.org/10.1007/s11232-015-0312-0

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