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Position-dependent mass Schrödinger equations allowing harmonic oscillator (HO) eigenvalues

Authors

  • J. J. Peña,

    Corresponding author
    1. Universidad Autónoma Metropolitana - Azcapotzalco, CBI - Area de Fsica Atómica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 México, D. F
    • Universidad Autónoma Metropolitana - Azcapotzalco, CBI - Area de Fsica Atómica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 México, D. F
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  • G. Ovando,

    1. Universidad Autónoma Metropolitana - Azcapotzalco, CBI - Area de Fsica Atómica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 México, D. F
    2. Escuela Superior de Fsica y Matemáticas, IPN, Unidad Profesional Adolfo López Mateos Zacatenco, Edificio 9, 07738 México, D.F
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  • J. Morales,

    1. Universidad Autónoma Metropolitana - Azcapotzalco, CBI - Area de Fsica Atómica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 México, D. F
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  • J. GarcÍa-Ravelo,

    1. Escuela Superior de Fsica y Matemáticas, IPN, Unidad Profesional Adolfo López Mateos Zacatenco, Edificio 9, 07738 México, D.F
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  • C. Pacheco-García

    1. Escuela Superior de Fsica y Matemáticas, IPN, Unidad Profesional Adolfo López Mateos Zacatenco, Edificio 9, 07738 México, D.F
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Abstract

Quantum chemical systems with a position-dependent mass have attracted the attention due to their relevance in describing the features of many microstructures of current interest. In this work, the point canonical transformation method applied to Schrödinger equations with a position-dependent mass (SEPDM) is presented. Essentially, the proposal is aimed to transform the Schrödinger equation with a position-dependent mass into a standard Schrödinger-like equation for constant mass in such a way that the position-dependent mass distribution (PDMD) becomes incorporated into the effective potential. As an useful application of the proposal, it is considered as effective potential the one-dimensional harmonic oscillator potential model, which leads to those isospectral potentials related to different forms of PDMD. For example, the exactly solvable isospectral potentials involved in the SEPDM for some PDMD such as equation image, equation image, equation image, equation image, equation image, xα, and equation image, are worked out explicitly including their raising and lowering operators that factorize the SEPDM for each PDMD allowing HO eigenvalues. However, the proposal is general and can be straightforwardly applied to other effective potential models as well as other PDMD that could be useful in quantum chemical applications. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

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