Delta-like singularity in the Reduction of the Laplace Equation for Spherical Coordinates and the Validity of Radial Schrodinger Equation

2010/07/31 by Anzor Khelashvili, Anzor A. Khelashvili, Khelashvili, Anzor A. +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Elasticity and Wave Propagation #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Numerical methods for differential equations #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1008.0086

7 pages

arxiv created 2010/07/31 · openalex publication_date 2010/07/31 · arxiv updated 2010/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By careful exploration of separation of variables into the Laplacian in spherical coordinates, we obtain the extra delta-like singularity, elimination of which restricts the radial wave function at the origin. This constraint has the form of boundary condition for the radial Schrodinger equation.

Related

• Delta function singularity in the Reduction of Radial Schrodinger Equation
• Unexpected Delta-Function Term in the Radial Schrodinger Equation
• On the appearance of a Dirac delta term at the origin in the Schroedinger radial equation
• Behaviour of the wave function near the origin in the radial case
• Solutions of the Schrödinger equation, boundary condition at the origin, and theory of distributions