Weak- and strong-expansions of coherent states eigenfunctions for the generalized q-deformed harmonic oscillator and their completeness relations. (11th November 2021) - Yahiaoui, Sid-Ahmed
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 ( s → 0 ) 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, ( s → ∞ ), 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 ϑ 3 -function.