On the ladder operators and nonclassicality of generalized coherent state associated with a particle in an infinite square well

TL;DR

This paper develops ladder operators for a quantum particle in an infinite well, constructs associated coherent states, and explores their nonclassical properties and potential generation methods.

Contribution

It introduces a new pair of ladder operators linked to the infinite well, connects them with $su(1,1)$ algebra, and constructs related coherent states with nonclassical features.

Findings

Ladder operators are explicitly constructed for the infinite well.

Coherent states exhibit nonclassical properties such as squeezing.

A scheme for generating Gilmore-Perelomov coherent states is proposed.

Abstract

In this paper the factorization method is used in order to obtain the eigenvalues and eigenfunctions of a quantum particle confined in a one-dimensional infinite well. The output results from the mentioned approach allows us to explore an appropriate new pair of raising and lowering operators corresponding to the physical system under consideration. From the symmetrical considerations, the connection between the obtained ladder operators with $su(1,1)$ Lie algebra is explicitly established. Next, after the construction of Barut-Girardello and Gilmore-Perelomov representations of coherent states associated with the considered system, some of their important properties like the resolution of the identity including a few nonclassical features are illustrated in detail. Finally, a theoretical scheme for generation of the Gilmore-Perelomov type of coherent state via a generalized Janes-Cummings model is proposed.