Fractional supersymmetry and hierarchy of shape invariant potentials

Maurice Robert Kibler (1) , Mohammed Daoud (1)

1 IPNL - Institut de Physique Nucléaire de Lyon

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.

Mots clés: fractional supersymmetry; supersymmetric quantum mechanics; shape invariance potentials; Weyl-Heisenberg algebra

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]

Maurice Robert Kibler, Mohammed Daoud. Fractional supersymmetry and hierarchy of shape invariant potentials. Journal of Mathematical Physics, 2006, 47, pp.122108. ⟨10.1063/1.2401711⟩. ⟨in2p3-00090893v3⟩