Group theoretical approach to the intertwined Hamiltonians
Cariñena, José F. ; C., David J. Fernández ; Ramos, Arturo
arXiv, 0311029 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-11-20
Classification:  Mathematical Physics,  High Energy Physics - Theory,  Quantum Physics 
@article{0311029,
     author = {Cari\~nena, Jos\'e F. and C., David J. Fern\'andez and Ramos, Arturo},
     title = {Group theoretical approach to the intertwined Hamiltonians},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0311029}
}

Cariñena, José F.; C., David J. Fernández; Ramos, Arturo. Group theoretical approach to the intertwined Hamiltonians. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0311029/