Quantum algebra from generalized q-Hermite polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:480

Article

Mezlini, Kamel¹  Azaiez, Najib Ouled^2,3 

[1] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Tunis El Manar 2092, Tunisia

[2] Univ Sfax, Fac Sci Sfax, Dept Math, BP 1171, Sfax 3000, Tunisia

[3] King Faisal Univ, Coll Sci, Dept Math, POB 400, Al Hasa 31982, Saudi Arabia

关键词: q-orthogonal polynomials;    q-deformed algebras;    Harmonic oscillators;   

DOI  :  10.1016/j.jmaa.2019.07.047

来源: Elsevier

【 摘 要 】

In this paper, we discuss new results related to the generalized discrete q-Hermite II polynomials (h) over tilde (n,alpha)(x; q), introduced by Mezlini et al. in 2014. Our aim is to give a continuous orthogonality relation, a q-integral representation and an evaluation at unity of the Poisson kernel, for these polynomials. Furthermore, we introduce q-Schrodinger operators and we give the raising and lowering operator algebra corresponding to these polynomials. Our results generate a new explicit realization of the quantum algebra su(q)(1, 1), using the generators associated with a q-deformed generalized para-Bose oscillator. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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