2009/06/01 by Wang-Chang Su
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Algebraic structure #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Realization (probability) #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/42/38/385202
20 pages
arxiv created 2009/06/01 · openalex publication_date 2009/09/01 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Within the framework of supersymmetric quantum mechanics, we study the simplified version of the potential algebra of the shape invariance condition in k steps, where k is an arbitrary positive integer. The associated potential algebra is found to be equivalent to the generalized deformed oscillator algebra that has a built-in Z k -grading structure. The algebraic realization of the shape invariance condition in k steps is therefore formulated by the method of the Z k -graded deformed oscillator. Based on this formulation, we explicitly construct the general algebraic properties for shape invariant potentials in k steps, in which the parameters of partner potentials are related to each other by the translation a 1 = a 0 + δ. The obtained results include the cyclic shape invariant potentials of period k as a special case.