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A large class of bound-state solutions of the Schrödinger equation via Laplace transform of the confluent hypergeometric equation

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Abstract

It is shown that analytically soluble bound states of the Schrödinger equation for a large class of systems relevant to atomic and molecular physics can be obtained by means of the Laplace transform of the confluent hypergeometric equation. It is also shown that all closed-form eigenfunctions are expressed in terms of generalized Laguerre polynomials. The generalized Morse potential is used as an illustration.

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Acknowledgments

This work was supported in part by means of funds provided by FAPESP, CNPq and CAPES.

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Authors and Affiliations

  1. Departamento de Física e Química, Universidade Estadual Paulista, Campus de Guaratinguetá, Guaratinguetá, SP, 12516-410, Brazil

    P. H. F. Nogueira & A. S. de Castro

  2. Departamento de Física Experimental, Instituto de Física, Universidade de São Paulo, São Paulo, SP, 05508-090, Brazil

    D. R. M. Pimentel

Authors
  1. P. H. F. Nogueira
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  2. A. S. de Castro
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  3. D. R. M. Pimentel
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Correspondence to A. S. de Castro.

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Nogueira, P.H.F., de Castro, A.S. & Pimentel, D.R.M. A large class of bound-state solutions of the Schrödinger equation via Laplace transform of the confluent hypergeometric equation. J Math Chem 54, 1287–1295 (2016). https://doi.org/10.1007/s10910-016-0621-z

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  • DOI: https://doi.org/10.1007/s10910-016-0621-z

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