2009/05/31 by Bijan Bagchi, Toshiaki Tanaka
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1016/j.aop.2009.08.002
published as Annals Phys.324:2438-2451,2009 · 17 pages, no figures; minor corrections, to appear in Annals of Physics
openalex publication_date 2009/08/14 · arxiv created 2009/08/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Type A N-fold supercharge admits a one-parameter family of factorizations into product of N first-order linear differential operators due to an underlying GL(2,C) symmetry. As a consequence, a type A N-fold supersymmetric system can have different intermediate Hamiltonians corresponding to different factorizations. We derive the necessary and sufficient conditions for the latter system to possess intermediate Hamiltonians for the N=2 case. We then show that whenever it has (at least) one intermediate Hamiltonian, it can admit second-order parasupersymmetry and a generalized 2-fold superalgebra. As an illustration, we construct a set of generalized Poeschl--Teller potentials of this kind.