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Singular behavior of the Laplace operator in spherical coordinates isinvestigated. It is shown that in course of transition to the reduced radialwave function in the Schrodinger equation there appears additional termconsisting the Dirac delta function, which was unnoted during the full historyof physics and mathematics. The possibility of avoiding this contribution fromthe reduced radial equation is discussed. It is demonstrated that for this aimthe necessary and sufficient condition is requirement the fast enough fallingof the wave function at the origin. The result does not depend on character ofpotential:is it regular or singular. The various manifestations andconsequences of this observation are considered as well. The cornerstone in ourapproach is the natural requirement that the solution of the radial equation atthe same time must obey to the full equation.

physics of particles and nuclei letters

Singular Behavior of the Laplace Operator in Polar Spherical Coordinates  and Some of Its Consequences for the Radial Wave Function at the Origin of  Coordinates