Hurwitz's matrices, Cayley transformation and the Cartan-Weyl basis for the orthogonal groups
| dc.creator | Hassan, Mehdi Hage | |
| dc.date | 2006-10-10 | |
| dc.date.accessioned | 2026-07-07T07:28:27Z | |
| dc.date.available | 2026-07-07T07:28:27Z | |
| dc.description | We find the transformations from the basis of the hydrogen atom of n-dimensions to the basis of the harmonic oscillator of N=2(n-1) dimensions using the Cayley transformation and the Hurwitz matrices. We prove that the eigenfunctions of the Laplacian ∆n are also eigenfunctions of the Laplacien ∆N for n=1, 3, 5 and 9. A new parameterization of the transformation R8->R5 is derived. This research leads us first to a new class of spherical functions of the classical groups we call it the bispherical harmonic functions. Secondly: the development of Hurwitz's matrix in terms of adjoint representation of the Cartan-Weyl basis for the orthogonal groups SO(n) leads to what we call the generating matrices of the Cartan-Weyl basis and then we establish it for n=2,4,8,... . | |
| dc.identifier | https://arxiv.org/abs/math-ph/0610021 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0610021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117737 | |
| dc.subject | Mathematical Physics | |
| dc.title | Hurwitz's matrices, Cayley transformation and the Cartan-Weyl basis for the orthogonal groups | |
| dc.type | text |