A note about the factorization of the angular part of the Laplacian and its application to the time-independent Schrödinger equation

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dc.creatorAlayon-Solarz, Daniel
dc.date2007-05-01
dc.date2007-05-04
dc.date.accessioned2026-07-07T07:59:14Z
dc.date.available2026-07-07T07:59:14Z
dc.descriptionRemoving al least one point from the unit sphere in $ R^{3}$ allows to factorize the angular part of the laplacian with a Cauchy-Riemann type operator. Solutions to this operator define a complex algebra of potential functions. A family of these solutions is shown to be normalizable on the sphere so it is possible to construct associate solutions for every radial solution to the time-independant Schrödinger equation with a radial potential, such that this family of solutions is square integrable in $R^{3}$. While this family of associated solutions are singular on at least one half-plane, they are square-integrable in almost all of $R^{3}$.
dc.description4 pages
dc.identifierhttps://arxiv.org/abs/0705.0071
dc.identifierhttp://arxiv.org/abs/0705.0071
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128292
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectComplex Variables
dc.titleA note about the factorization of the angular part of the Laplacian and its application to the time-independent Schrödinger equation
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