2001/08/01 by José F. Cariñena, Arturo Ramos, David J. Fernández C. +1 · 1 citation
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1006/aphy.2001.6179
published as Annals Phys. 292 (2001) 42-66
arxiv created 2003/11/20 · arxiv updated 2009/12/01
We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered by two of us in a previous paper. Then, we give a group theoretical explanation to the problem of Hamiltonians related by a first order differential operator. A generalization of the finite difference algorithm relating eigenfunctions of \emph three different Hamiltonians is found, and some illustrative examples of the theory are analyzed, finding new potentials for which one eigenfunction and its corresponding eigenvalue is exactly known.