English

Fractional supersymmetry algebra and lacunary Hermite polynomials

High Energy Physics - Theory 2019-06-27 v2 Quantum Algebra

Abstract

We consider a realization of fractional supersymmetric of quantum mechanics of order rr, where the Hamiltonian and supercharges involve reflection operators. It is shown that the Hamiltonian has rr-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.

Keywords

Cite

@article{arxiv.1810.08275,
  title  = {Fractional supersymmetry algebra and lacunary Hermite polynomials},
  author = {F. Bouzeffour and M. Garayev},
  journal= {arXiv preprint arXiv:1810.08275},
  year   = {2019}
}