Delta function singularity in the Reduction of Radial Schrodinger Equation

TL;DR

This paper identifies a delta-like singularity arising during the reduction of the Laplace operator in spherical coordinates, which influences the boundary conditions of radial wave functions in quantum mechanics.

Contribution

It reveals an extra delta-like singularity in the reduction process, clarifying its impact on boundary conditions for radial wave functions.

Findings

Discovery of a delta-like singularity in the Laplace operator reduction.

Implication of this singularity on boundary conditions at the origin.

Clarification of restrictions on radial wave functions.

Abstract

We obtain the extra delta-like singularity while reduction of the Laplace operator in spherical coordinates, elimination of which restricts the radial wave functions at the origin. This restriction has the form of boundary condition for the radial wave function.