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Exact solution of the semiconfined harmonic oscillator model with a position-dependent effective mass

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Abstract

We present a new model of a one-dimensional nonrelativistic canonical quantum harmonic oscillator which is semiconfined. Semiconfinement is achieved by replacing the constant effective mass with a mass that varies with position. The problem is exactly solvable and the analytic expression of the wavefunctions of the stationary states is expressed by means of generalized Laguerre polynomials. Surprisingly, the energy spectrum completely overlaps with the energy spectrum of the standard nonrelativistic canonical quantum harmonic oscillator. In the limit when the semiconfinement parameter a goes to infinity, the wavefunctions also tend to the wavefunction of the standard oscillator in terms of Hermite polynomials.

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Acknowledgements

E.I. Jafarov kindly acknowledges that this work was supported by the Science Development Foundation under the President of the Republic of Azerbaijan—Grant Nr EIF-KETPL-2-2015-1(25)-56/01/1. J. Van der Jeugt was supported by the EOS Research Project 30889451.

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Authors and Affiliations

  1. Institute of Physics, Azerbaijan National Academy of Sciences, Javid ave. 131, AZ1143, Baku, Azerbaijan

    E. I. Jafarov

  2. Department of Applied Mathematics, Computer Science and Statistics, Faculty of Sciences, Ghent University, Krijgslaan 281-S9, 9000, Gent, Belgium

    J. Van der Jeugt

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  1. E. I. Jafarov
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Correspondence to E. I. Jafarov.

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Jafarov, E.I., Van der Jeugt, J. Exact solution of the semiconfined harmonic oscillator model with a position-dependent effective mass. Eur. Phys. J. Plus 136, 758 (2021). https://doi.org/10.1140/epjp/s13360-021-01742-z

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