The Husimi function of a semiconfined harmonic oscillator model with a position-dependent effective mass

We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute the Wigner distribution function exactly for such a semiconfinement quantum system. This method suppresses the divergence of the integrand in the definition of the quantum distribution function and leads to the computation of its analytical expressions for the stationary states of the semiconfined oscillator model. For this quantum system, both the presence and absence of the applied external homogenous field are studied. Obtained exact expressions of the Wigner distribution function are expressed through the Bessel function of the first kind and Laguerre polynomials. Furthermore, some of the special cases and limits are discussed in detail.

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On the construction of the coherent states of the semiconfined harmonic oscillator with a position-dependent effective mass

Nagiyev,

Jafarov

2024

J. Phys.: Conf. Ser.

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We present details of the method for constructing the coherent states of the quantum harmonic oscillator model that exhibits the semiconfinement effect due to a specific change of its mass by position. Its energy spectrum completely overlaps with the Hermite oscillator energy spectrum, whereas the wavefunctions of the stationary states are expressed via the generalized Laguerre polynomials. Two different methods have been applied to compute the coherent states. They are generalized and Barut-Girardello coherent states methods. In both cases, the exact expressions have been obtained. We also analyzed some limit cases, under which the constructed coherent states completely recover the coherent states of the Hermite oscillator.

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The Husimi function of a semiconfined harmonic oscillator model with a position-dependent effective mass

Cited by 4 publications

References 83 publications

Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass

Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass

The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass

On the construction of the coherent states of the semiconfined harmonic oscillator with a position-dependent effective mass

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