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

TL;DR

This paper constructs the phase space Husimi distribution for a semiconfined harmonic oscillator with position-dependent mass, analyzing stationary states with and without external fields, and discusses special cases and limits.

Contribution

It introduces a novel phase space representation for a semiconfined oscillator with variable mass, deriving the Husimi function explicitly for stationary states.

Findings

Husimi distribution expressed via double sum of parabolic cylinder functions

Analysis of special cases and limit relations

Extension to cases with external homogeneous fields

Abstract

The phase space representation for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. We have found the Husimi distribution function for the stationary states of the oscillator model under consideration for both cases without and with the applied external homogeneous field. The obtained function is expressed through the double sum of the parabolic cylinder function. Different special cases and the limit relations are discussed, too.