The hydrogen atom according to wave mechanics - III. ellipsoidal coordinates
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| Author: | |
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| Format: | artículo original |
| Status: | Versión publicada |
| Publication Date: | 2017 |
| Description: | Schroedinger's temporally independent partial-differential equation is directly solvable in ellipsoidal coordinates to yield three ordinary-differential equations; with a common factor in equatorial angular coordinate φ as in spherical polar and paraboloidal coordinates, the product of their solutions contains confluent Heun functions in coordinates ξ and η that impede further calculations at present. To provide plots of these functions, we apply published solutions from Kereselidze et al. in series to illustrate the dependence of the shape of the amplitude functions on distance d between the foci of the ellipsoids, between limiting cases of amplitude functions in spherical polar coordinates as d → 0 and in paraboloidal coordinates as d → ∞. These ellipsoidal coordinates are most appropriate for a treatment of a hydrogen atom in a diatomic-molecular context. |
| Country: | Portal de Revistas UCR |
| Institution: | Universidad de Costa Rica |
| Repositorio: | Portal de Revistas UCR |
| Language: | Español |
| OAI Identifier: | oai:portal.ucr.ac.cr:article/29660 |
| Online Access: | https://revistas.ucr.ac.cr/index.php/cienciaytecnologia/article/view/29660 |
| Keyword: | átomo de hidrógeno mecánica de onda coordenadas elipsoidales orbitales espectro atómico hydrogen atom wave mechanics ellipsoidal coordinates orbitals atomic spectra |