Barut-Girardello and Gilmore-Perelomov coherent states for pseudoharmonic oscillator and their nonclassical properties: factorization method

TL;DR

This paper constructs and analyzes Barut-Girardello and Gilmore-Perelomov coherent states for the pseudoharmonic oscillator using the factorization method, revealing their nonclassical properties and underlying SU(1,1) symmetry.

Contribution

It introduces ladder operators for the pseudoharmonic oscillator and constructs two classes of coherent states, highlighting their nonclassical features and symmetry structure.

Findings

Successfully derived ladder operators via factorization

Constructed two classes of coherent states for the system

Numerically demonstrated nonclassical properties

Abstract

In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schr\"{o}dinger equation by using the factorization method. The obtained generalized raising and lowering operators naturally lead us to the Dirac representation space of the system which is very easier to work with, in comparison to the functional Hilbert space. The SU(1,1) dynamical symmetry group associated with the considered system is exactly established through investigating the fact that the deduced operators satisfy appropriate commutation relations. This result enables us to construct two important and distinct classes of Barut-Girardello and Gilmore-Perelomov coherent states associated with the system. Finally, their identities as the most important task are exactly resolved and some of their nonclassical properties are illustrated, numerically.