# 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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