Unified treatment of exactly solvable quantum potentials with confluent hypergeometric eigenfunctions: Generalized potentials

Authors

  • J. J. Peña,

    Corresponding author
    1. Universidad Autónoma Metropolitana—Azcapotzalco, DCB, Area de Física Atómica Molecular Aplicada, Av. San Pablo 180, 02200 México, D.F., Mexico
    • Universidad Autónoma Metropolitana—Azcapotzalco, DCB, Area de Física Atómica Molecular Aplicada, Av. San Pablo 180, 02200 México, D.F., Mexico
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  • J. Morales,

    1. Universidad Autónoma Metropolitana—Azcapotzalco, DCB, Area de Física Atómica Molecular Aplicada, Av. San Pablo 180, 02200 México, D.F., Mexico
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  • J. García-Martínez,

    1. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional—Zacatenco, Edificio 9, Unidad Profesional Adolfo López Mateos, 07738 México, D.F., Mexico
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  • J. García-Ravelo

    1. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional—Zacatenco, Edificio 9, Unidad Profesional Adolfo López Mateos, 07738 México, D.F., Mexico
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Abstract

In this work, we propose an alternative approach to transform a general second-order differential equation (DE) into a Schrödinger-like equation. As a useful application of the proposal, we consider explicitly the case of the confluent hypergeometric (CH) DE with the aim to unify all potentials having CH eigenfunctions. That is, the proposed approach allows us to obtain generalized potential models that contain as particular cases the standard exactly solvable potentials with CH solutions such as the one- and three-dimensional Harmonic, Morse, Coulomb, and other well known potentials. Besides, due that the proposed method is general, it can be straightforwardly applied to other DE in the search of bound-states solutions for new potential models that could be useful in quantum chemistry. © 2012 Wiley Periodicals, Inc.

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