Group theoretical approach to the intertwined Hamiltonians

Details Group theoretical approach to the intertwined Hamiltonians Group theoretical approach to the intertwined Hamiltonians

2003-11-20

arxiv.org/abs/math-ph/0311029v1

Annals Phys. 292 (2001) 42-66

Physics

Mathematical Physics

Scientific paper

10.1006/aphy.2001.6179

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.

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