A set of nonlinear coherent states for the pseudoharmonic oscillator

2019/07/20 by Khalid Ahbli, Hamidou Kassogué, Ahbli, Khalid +4
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1907.08881

openalex publication_date 2019/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct two-parameters family of nonlinear coherent states by replacing the factorial in coefficients zⁿ/√(n!) of the canonical coherent states by a specific generalized factorial x_n^γ,σ! where parameters γ and σ 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 γ and σ, we attache these states to the pseudo-harmonic oscillator depending on two parameters α,β> 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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