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

Abstract

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.

Higher-order phase-space moments for off-diagonal rotating Morse oscillators

“…Our results in this paper, as in the previous work [1], were limited to a Hermitian Morse oscillator with a constant-mass. Therefore, a natural extension of these works would be to consider quantum systems with position-dependent mass (PDM) [28], subjected to either PT-symmetric or pseudo-hermiticity [31][32][33], to examine how the PDM-function M(x) and the discrete symmetry pseudo hermiticity  affect moment measurements. Some of these ideas are currently in progress.…”

“…As in the previous paper [1], the Wigner distribution function (WDF) [26][27][28] for the wave-functions (6) can be evaluated in straightforward manner in the basis |n, J〉 by substituting equation (6) into the expression, which gives…”