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Generalized semiconfined harmonic oscillator model with a position-dependent effective mass

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Abstract

By using a point canonical transformation starting from the constant-mass Schrödinger equation for the isotonic potential, it is shown that a semiconfined harmonic oscillator model with a position-dependent mass in the BenDaniel–Duke setting and the same spectrum as the standard harmonic oscillator can be easily constructed and extended to a semiconfined shifted harmonic oscillator, which could result from the presence of a uniform gravitational field. A further generalization is proposed by considering a m-dependent position-dependent mass for \(0<m<2\) and deriving the associated semiconfined potential. This results in a family of position-dependent mass and potential pairs, to which the original pair belongs as it corresponds to \(m=1\). Finally, the potential that would result from a general von Roos kinetic energy operator is presented and the examples of the Zhu–Kroemer and Mustafa–Mazharimousavi settings are briefly discussed.

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Notes

  1. Note that we have adopted here units wherein \(\hbar = 2m_0\) in the original paper.

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Acknowledgements

This work was supported by the Fonds de la Recherche Scientifique-FNRS under Grant No. 4.45.10.08.

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  1. Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050, Brussels, Belgium

    C. Quesne

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Quesne, C. Generalized semiconfined harmonic oscillator model with a position-dependent effective mass. Eur. Phys. J. Plus 137, 225 (2022). https://doi.org/10.1140/epjp/s13360-022-02444-w

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