Displacement and Squeeze Operators of a Three-Dimensional Harmonic Oscillator and Their Associated Quantum States

TL;DR

This paper extends the concepts of displacement and squeeze operators to three-dimensional harmonic oscillators, constructing related quantum states and analyzing their properties including Wigner functions and squeezing parameters.

Contribution

It introduces a generalized framework for 3D harmonic oscillator operators and constructs associated coherent and squeezed states, along with their phase space and quantum statistical properties.

Findings

Derived the 3D displacement and squeeze operators.

Constructed coherent and squeezed states for 3D harmonic oscillators.

Analyzed the Wigner function and quantum statistical properties.

Abstract

We generalized the squeeze and displacement operators of the one-dimensional harmonic oscillator to the three-dimensional case and based on these operators we construct the corresponding coherent and squeezed states. We have also calculated the Wigner function for the three-dimensional harmonic oscillator and from the analysis of time evolution of this function, the quantum Liouville equation is also presented. Further properties of the quantum states including Mandel's Q and quadrature squeezing parameters are discussed as well.