Weak and strong expansions of the generalized q-deformed coherent states approximate eigenfunctions and its resolution of unity

TL;DR

This paper derives explicit expressions for generalized q-deformed harmonic oscillator coherent states using weak and strong expansion methods, and constructs their resolution of unity, advancing understanding of q-deformed quantum states.

Contribution

It introduces explicit weak and strong expansion formulas for q-deformed coherent states and details their resolution of unity, enhancing analytical tools for q-deformed quantum systems.

Findings

Explicit weak and strong expansion formulas derived.

Resolution of unity constructed for the states.

Connections between weak and strong limits established.

Abstract

The aim of this paper is to provide an explicit expressions for the generalized q-deformed harmonic oscillator coherent states obtained in terms of a weak and strong behavior expansions. We first use the weak (s --> 0) deformed version of q-boson annihilation operator to solve Barut-Girardello's eigenvalues coherent states equation for the generalized q-deformed harmonic oscillator. In strong behavior limit (s --> 1) the previous result is resumed using the variational perturbation theory. We also describe the construction of their resolution of unity.