1992/12/23 by Avinash Khare, A. Khare, U. Sukhatme +1 · 3 citations
Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th
paper · pdf · doi:10.1088/0305-4470/26/18/003
published as J.Phys. A26 (1993) L901-L904 · 8pages, TeX
arxiv created 1992/12/23 · openalex publication_date 1993/09/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, the authors obtain a large class of new shape-invariant potentials which are reflectionless and possess an infinite number of bound states. They can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for energy eigenvalues, eigenfunctions and transmission coefficients are given. Included in the potentials as a special case is the self-similar potential recently discussed by Shabat (1992) and Spiridonov (1992).