Fractional supersymmetry and hierarchy of shape invariant potentials

2006/09/30 by M. Daoud, Maurice Robert Kibler, Mohammed Daoud +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1063/1.2401711

published as J.Math.Phys.47:122108,2006 · 15 pages; version 2: introduction and conclusion enlarged, acknowledgment added, references added; version 3: one reference added

arxiv created 2006/11/07 · openalex publication_date 2006/12/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• An algebraicq-deformed form for shape-invariant systems
• Two-dimensional fractional supersymmetry from the quantum Poincaré group at roots of unity
• MAPPING OF NON-CENTRAL POTENTIALS UNDER POINT CANONICAL TRANSFORMATIONS
• Nontrivial Extensions of the 3D-Poincaré Algebra and Fractional Supersymmetry for Anyons
• New shape-invariant potentials in supersymmetric quantum mechanics
• Supersymmetry and Quantum Mechanics

Cited by

• Algebraic shape invariant potentials as the generalized deformed oscillator