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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 $R^{3}$.

A note about the factorization of the angular part of the Laplacian and its application to the time-independent Schr\"odinger equation