Fractional supersymmetry algebra and lacunary Hermite polynomials

2018/10/19 by Fethi Bouzeffour, F. Bouzeffour, Bouzeffour, F. +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.1810.08275

openalex publication_date 2018/10/19 · arxiv created 2019/06/26 · arxiv updated 2019/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a realization of fractional supersymmetric of quantum mechanics of order r, where the Hamiltonian and supercharges involve reflection operators. It is shown that the Hamiltonian has r-fold degenerate spectrum and the eigenvalues of hermitian supercharges are zeros of the associated Hermite polynomials of Askey and Wimp. Also it is shown that the associated eigenfunctions involve lacunary Hermite polynomials.

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