Group theoretical approach to the intertwined Hamiltonians
Mathematical Physics
2007-05-23 v1 High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
We show that the finite difference B\"acklund formula for the Schr\"odinger 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.
Cite
@article{arxiv.math-ph/0311029,
title = {Group theoretical approach to the intertwined Hamiltonians},
author = {José F. Cariñena and David J. Fernández C. and Arturo Ramos},
journal= {arXiv preprint arXiv:math-ph/0311029},
year = {2007}
}