Khalid Ahbli

Bio: Khalid Ahbli is an academic researcher. The author has contributed to research in topics: Coherent states & Orthogonal polynomials. The author has an hindex of 2, co-authored 8 publications receiving 11 citations.

A generating function and formulae defining the first-associated Meixner–Pollaczek polynomials

Abstract: While considering nonlinear coherent states with anti-holomorphic coefficients z¯n/xn!, we identify as first-associated Meixner–Pollaczek polynomials the orthogonal polynomials arising from...

Orthogonal polynomials attached to coherent states for the symmetric Poschl-Teller oscillator

Abstract: We consider a one-parameter family of nonlinear coherent states by replacing the factorial in coefficients of the canonical coherent states by a specific generalized factorial depending on a parameter gamma. These states are superposition of eigenstates of the Hamiltonian with a symmetric Poschl-Teller potential depending on a parameter nu > 1. The associated Bargmann-type transform is defined for equal parameters. Some results on the infinite square well potential are also derived. For some different values of gamma, we discuss two sets of orthogonal polynomials that are naturally attached to these coherent states.

Nonlinear Coherent States Associated with a Measure on the Positive Real Half Line

Abstract: We construct a class of generalized nonlinear coherent states by means of a newly obtained class of 2D complex orthogonal polynomials. The associated Bargmann-type transform is discussed. A polynomials realization of the basis of the quantum states Hilbert space is also obtained. Here, the entire structure owes its existence to a certain measure on the positive real half line, of finite total mass, together with all its moments. We illustrate this method with the measure $$r^\beta e^{-r}dr$$, where $$\beta $$ is a non-negative constant, which leads to a new generalization of the true-polyanalytic Bargmann transform.

A new generalization of nonlinear coherent states for the pseudoharmonic oscillator

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 pseudoharmonic 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.

Research Article Orthogonal polynomials attached to coherent states for the symmetric Pöschl–Teller oscillator

Abstract: We consider a one-parameter family of nonlinear coherent states by replacing the factorial in coefficients zn/n! of the canonical coherent states by a specific generalized factorial xnγ!, γ≥0. These states are superposition of eigenstates of the Hamiltonian with a symmetric Poschl–Teller potential depending on a parameter ν>1. The associated Bargmann-type transform is defined for γ=ν. Some results on the infinite square well potential are also derived. For some different values of γ, we discuss two sets of orthogonal polynomials that are naturally attached to these coherent states.

Table Of Integrals Series And Products

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Meixner-Pollaczek polynomials and the Heisenberg algebra

Abstract: An alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. Phys. 28, 509 (1987)]. The continuous Hahn polynomials turn out to be Meixner–Pollaczek polynomials. Use is made of the connection between Laguerre polynomials and Meixner–Pollaczek polynomials, the Rodrigues formula for Laguerre polynomials, an operational formula involving Meixner–Pollaczek polynomials, and the Schrodinger model for the irreducible unitary representations of the three‐dimensional Heisenberg group.

Generating functions of Pollaczek polynomials: a revisit

Abstract: This paper is mainly devoted to generating functions of Pollaczek and other related polynomials. We first present a new proof of Wimp's formula for the associated Pollaczek polynomials Pnλz;a,b,c. ...

A generating function and formulae defining the first-associated Meixner–Pollaczek polynomials

Abstract: While considering nonlinear coherent states with anti-holomorphic coefficients z¯n/xn!, we identify as first-associated Meixner–Pollaczek polynomials the orthogonal polynomials arising from...