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Group theoretical approach to the intertwined Hamiltonians

José F. Cariñena·David J. Fernández C.·Arturo Ramos
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Abstract

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.

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BibTeXRIS

José F. Cariñena, David J. Fernández C., Arturo Ramos. 2003-11-20. Group theoretical approach to the intertwined Hamiltonians. https://doi.org/10.1006/aphy.2001.6179

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