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Fractional Supersymmetric Hermite Polynomials

Author

Listed:
  • 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
    Faculté des Sciences de Tunis, LR11ES11 Laboratoire d’Analyse Mathématiques et Applications, Université de Tunis El Manar, Tunis 2092, Tunisia)

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.

Suggested Citation

  • Fethi Bouzeffour & Wissem Jedidi, 2020. "Fractional Supersymmetric Hermite Polynomials," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:193-:d:316598
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