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Fractional supersymmetry and hierarchy of shape invariant potentials

Maurice Robert Kibler·Mohammed Daoud
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Abstract

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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Maurice Robert Kibler, Mohammed Daoud. 2006-11-07. Fractional supersymmetry and hierarchy of shape invariant potentials. https://doi.org/10.1063/1.2401711

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