The hydrogen atom -- wave mechanics beyond schroedinger, orbitals as algebraic formulae derived in all four coordinate systems

 

Guardado en:
Detalles Bibliográficos
Autor: Ogilvie, J. F.
Formato: artículo original
Estado:Versión publicada
Fecha de Publicación:2017
Descripción:Chemists are aware of the solution of Schroedinger's equations for the hydrogen atom in only spherical polar coordinates, but the spatial variables are separable also in three other systems - - paraboloidal, ellipsoidal and spheroconical; we report here explicit algebraic solutions directly derived in ellipsoidal and spheroconical coordinates for the first time. Our solutions progress from those previously known in spherical polar but not entirely understood, through those little known in paraboloidal, to those in systems of ellipsoidal and spheroconical coordinates unknown before the present work. Applications of these solutions include angular momenta, a quantitative calculation of the discrete absorption spectrum and accurate plots of surfaces of amplitude functions. The shape of a surface of a particular amplitude function, and even the quantum numbers in a particular set to specify such an individual function, depend on a particular chosen system of coordinates, and are therefore artefacts of that coordinate representation within wave mechanics; a choice of a coordinate system to discuss atomic or molecular properties based on the shapes of amplitude functions or their respective quantum numbers is hence arbitrary
País:Portal de Revistas UCR
Institución:Universidad de Costa Rica
Repositorio:Portal de Revistas UCR
Lenguaje:Español
OAI Identifier:oai:portal.ucr.ac.cr:article/29521
Acceso en línea:https://revistas.ucr.ac.cr/index.php/cienciaytecnologia/article/view/29521
Palabra clave:hydrogen atom
wave mechanics
spherical polar coordinates
paraboloidal coordinates
ellipsoidal coordinates
spheroconical coordinates
átomo de hidrógeno
mecánica de ondas
coordenadas polar esféricas
coordenadas paraboloides
coordenadas elipsoides
coordenadas esferocónicas