Fractional supersymmetry and hierarchy of shape invariant potentials

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.

15 pages; version 2: introduction and conclusion enlarged, acknowledgment added, references added; version 3: one reference added

References in corpus (1)

• Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics

Cited by in corpus (5)

• Variations on a theme of Heisenberg, Pauli and Weyl
• Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential
• SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
• Shape invariance and the exactness of quantum Hamilton-Jacobi formalism
• Bases for spin systems and qudits from angular momentum theory