Coherent state of the effective mass harmonic oscillator

TL;DR

This paper constructs and analyzes coherent states for an effective mass harmonic oscillator, exploring their properties, different mass functions, and Wigner functions, revealing they are generally not minimum uncertainty states.

Contribution

It introduces a method to construct coherent states for the effective mass harmonic oscillator with various mass functions, and studies their properties and phase space representations.

Findings

Coherent states are not generally minimum uncertainty states.

Closed form expressions for different mass functions are derived.

Wigner functions of these states are computed.

Abstract

We construct coherent state of the effective mass harmonic oscillator and examine some of its properties. In particular closed form expressions of coherent states for different choices of the mass function are obtained and it is shown that such states are not in general x-p uncertainty states. We also compute the associated Wigner functions.