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

Abstract

We develop 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 applied for the analytical computation of the Wigner distribution function for such a semiconfinement quantum system. The method allows for suppression of 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. Both cases of the presence and absence of the applied external homogeneous field for this quantum system are studied. Obtained exact expressions of the Wigner distribution function are expressed through the Bessel function of the first kind and Laguerre polynomials. Further, some of the special cases and limits are discussed in detail.Comment: 10 pages, 9 figure