Fractional Supersymmetric Hermite Polynomials

被引：3

作者：

Bouzeffour, Fethi ^{[1
]}

Jedidi, Wissem ^{[2
,3
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia

[2] King Saud Univ, Dept Stat & OR, POB 2455, Riyadh 11451, Saudi Arabia

[3] Univ Tunis El Manar, Lab Analyse Mathemat & Applicat LR11ES11, Fac Sci Tunis, Tunis 2092, Tunisia

来源：

MATHEMATICS | 2020年 / 8卷 / 02期

关键词：

orthogonal polynomials; difference-differential operator; supersymmetry; DEFORMED HEISENBERG ALGEBRA; POWER;

D O I：

10.3390/math8020193

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a realization of fractional supersymmetry quantum mechanics of order r, where the Hamiltonian and the supercharges involve the fractional Dunkl transform as a Klein type operator. We construct several classes of functions satisfying certain orthogonality relations. These functions can be expressed in terms of the associated Laguerre orthogonal polynomials and have shown that their zeros are the eigenvalues of the Hermitian supercharge. We call them the supersymmetric generalized Hermite polynomials.

引用

页数：13

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