The hydrogen atom via the four-dimensional spherical harmonics
Using the fact that the Schr¨odinger equation for the stationary states of the hydrogen atom is equivalent to an integral equation on the unitsphere in a four-dimensional space, the eigenvalues, the eigenfunctions, and a dynamical symmetry group for this problem are obtained fromthe four-dimensional...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | México |
| Institución: | Benemérita Universidad Autónoma de Puebla |
| Repositorio: | Redalyc-BUAP |
| OAI Identifier: | oai:redalyc.org:57053512 |
| Acceso en línea: | https://www.redalyc.org/articulo.oa?id=57053512 |
| Access Level: | acceso abierto |
| Palabra clave: | Física, Astronomía y Matemáticas four Hydrogen atom hidden symmetries dimensional spherical harmonics |
| Sumario: | Using the fact that the Schr¨odinger equation for the stationary states of the hydrogen atom is equivalent to an integral equation on the unitsphere in a four-dimensional space, the eigenvalues, the eigenfunctions, and a dynamical symmetry group for this problem are obtained fromthe four-dimensional spherical harmonics and the group of rotations on the sphere. It is shown that the four-dimensional spherical harmonicsseparable in Euler angles correspond to solutions of the time-independent Schr¨odinger equation that are separable in parabolic coordinates. |
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