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arXiv · 1907.08881

A set of nonlinear coherent states for the pseudoharmonic oscillator

Khalid Ahbli·Hamidou Kassogue·Patrick K. Kayupe·Abdelhak Kouraich
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Abstract

We construct two-parameters family of nonlinear coherent states by replacing the factorial in coefficients $z^n/\sqrt{n!}$ of the canonical coherent states by a specific generalized factorial $x_n^{\gamma,\sigma}!$ where parameters $\gamma$ and $\sigma$ satisfy some conditions for which the normalization condition and the resolution of identity are verified. The obtained family is a generalization of the Barut-Girardello coherent states and those of the philophase states. In the particular case of parameters $\gamma$ and $\sigma$, we attache these states to the pseudo-harmonic oscillator depending on two parameters $\alpha,\beta> 0$. The obtained nonlinear coherent states are superposition of eigenstates of this oscillator. The associated Bargmann-type transform is defined and we derive some results.

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Khalid Ahbli, Hamidou Kassogue, Patrick K. Kayupe, Abdelhak Kouraich. 2019-07-20. A set of nonlinear coherent states for the pseudoharmonic oscillator. https://arxiv.org/abs/1907.08881

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