Coherent states in noncommutative quantum mechanics

TL;DR

This paper explores Gazeau-Klauder coherent states within noncommutative quantum mechanics, demonstrating their similarities to canonical coherent states and revealing their vector nature through an isometric mapping.

Contribution

It introduces and analyzes Gazeau-Klauder coherent states in noncommutative quantum mechanics, highlighting their properties and inherent vector features.

Findings

States saturate position uncertainty relation

States obey Poisson distribution

States have flat geometric structure

Abstract

Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.