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

A note about the factorization of the angular part of the Laplacian and its application to the time-independent Schrödinger equation - Mathematical Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: Removing al least one point from the unit sphere in $ R^{3}$ allows tofactorize the angular part of the laplacian with a Cauchy-Riemann typeoperator. Solutions to this operator define a complex algebra of potentialfunctions. A family of these solutions is shown to be normalizable on thesphere so it is possible to construct associate solutions for every radialsolution to the time-independant Schr\-odinger equation with a radialpotential, such that this family of solutions is square integrable in $R^{3}$.While this family of associated solutions are singular on at least onehalf-plane, they are square-integrable in almost all of $R^{3}$.

Author: ** Daniel Alayon-Solarz**

Source: https://arxiv.org/