Abstract
The explicit expressions for generalized q-deformed harmonic oscillator coherent states (q-DHO CS) obtained in terms of a weak- and strong-behavior expansions are investigated. We first employ the weak-deformed version () of q-boson annihilation operator to solve Barut-Girardello’s eigenvalues coherent states equation for generalized q-deformed harmonic oscillator, using for this some lemmas directly related to the resolution of Riccati differential equation. The similarity with the perturbation theory is established. In strong-behavior limit, (), the previous results are resumed using the variational perturbation theory, and the corresponding q-DHO CS are deduced. We also construct, in both limits, their associated completeness relations which turns out to be the elliptic Jacobi -function.
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