RICCATI EQUATION, FACTORIZATION METHOD AND SHAPE INVARIANCE

1999/10/14 by José F. Cariñena, J. F. Carinena, Arturo Ramos +1 · 5 citations
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP #msc:03.65.Fd #msc:11.30.Pb

paper · pdf · doi:10.1142/s0129055x00000502

published as Rev. Math. Phys. 12 (2000), 1279-1304 · Latex file, 35 pages

arxiv created 1999/10/14 · openalex publication_date 2000/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The basic concepts of factorizable problems in one-dimensional Quantum Mechanics, as well as the theory of Shape Invariant potentials are reviewed. The relation of this last theory with a generalization of the classical Factorization Method presented by Infeld and Hull is analyzed in detail. By the use of some properties of the Riccati equation the solutions of Infeld and Hull are generalized in a simple way.

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