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We present some details of the new model of the quantum harmonic oscillator that is semiconfined due to a specific change of its mass by position. We succeeded in solving exactly the Schrödinger equation corresponding to this model. Moreover, we found its dynamical symmetry algebra and could compute analytically its Kirkwood, Husimi and Wigner joint quasiprobability functions.

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The Semiconfined Harmonic Oscillator with a Position-Dependent Effective Mass: Exact Solution, Dynamical Symmetry Algebra and Quasiprobability Distribution Functions

  • 会议论文

  • 发表日期：

    2025年

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  • E. I. Jafarov,
  • S. M. Nagiyev,
  • J. Van der Jeugt

摘要

We present some details of the new model of the quantum harmonic oscillator that is semiconfined due to a specific change of its mass by position. We succeeded in solving exactly the Schrödinger equation corresponding to this model. Moreover, we found its dynamical symmetry algebra and could compute analytically its Kirkwood, Husimi and Wigner joint quasiprobability functions.