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...

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Detalles Bibliográficos
Autores: G. F. Torres del Castillo, J.L. Calvario Acócal
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
Descripción
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.