Fractional Supersymmetric Hermite Polynomials

Fethi Bouzeffour and Wissem Jedidi
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Fethi Bouzeffour: Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Wissem Jedidi: Department of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2020, vol. 8, issue 2, 1-13

Abstract: 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.

Keywords: orthogonal polynomials; difference-differential operator; supersymmetry (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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