Coherent States for the Isotropic and Anisotropic 2D Harmonic Oscillators

TL;DR

This paper introduces a novel method for constructing coherent states for 2D harmonic oscillators, including isotropic and anisotropic cases, using $SU(2)$ coherent states and analyzing their properties.

Contribution

It presents a new approach to generate coherent states for 2D oscillators via linear combinations of ladder operators and $SU(2)$ states, expanding the tools for quantum state analysis.

Findings

Constructed coherent states for 2D oscillators using $SU(2)$ states.

Analyzed uncertainty relations for the new states.

Studied probability density functions in configuration space.

Abstract

In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the $SU(2)$ coherent states, where these are then used as the basis of expansion for Schr\"odinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density functions in configuration space.