Infinite quantum well: a coherent state approach

TL;DR

This paper introduces a new family of vector-valued coherent states for a quantum particle in an infinite square well, enabling consistent phase space quantization and analysis of position and momentum observables.

Contribution

It presents a novel class of coherent states for the infinite well, facilitating phase space quantization and detailed operator analysis.

Findings

Coherent states enable consistent phase space quantization.

Position and momentum operators are well-defined within this framework.

Mean values and dispersions of observables are analyzed in these states.

Abstract

A new family of 2-component vector-valued coherent states for the quantum particle motion in an infinite square well potential is presented. They allow a consistent quantization of the classical phase space and observables for a particle in this potential. We then study the resulting position and (well-defined) momentum operators. We also consider their mean values in coherent states and their quantum dispersions.