Fractional supersymmetry and hierarchy of shape invariant potentials

@article{Kibler2006FractionalSA,
  title={Fractional supersymmetry and hierarchy of shape invariant potentials},
  author={Maurice R. Kibler and Mohammed Daoud},
  journal={Journal of Mathematical Physics},
  year={2006},
  volume={47},
  pages={122108}
}
Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra. The Hamiltonian gives rise to a hierarchy of isospectral Hamiltonians. Special cases of the algebra lead to dynamical systems for which the isospectral supersymmetric partner Hamiltonians are connected by a (translational or cyclic) shape invariance condition. 

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