Why Professor Richard Feynman was upset solving the Laplace equation for spherical waves?

TL;DR

This paper examines the singular behavior of the Laplace operator in spherical coordinates, explaining Feynman's frustration with solutions that exhibit fictitious singularities at the origin and proposing ways to resolve these issues.

Contribution

It clarifies the origin of Feynman's concerns by analyzing the singularities in Laplace solutions and offers methods to avoid these inconsistencies.

Findings

Identifies the source of fictitious singularities in classical Laplace solutions

Provides a method to eliminate these singularities at the origin

Enhances understanding of spherical wave solutions in physics

Abstract

We take attention to the singular behavior of the Laplace operator in spherical coordinates, which was established in our earlier work. This singularity has many non-trivial consequences. In this article we consider only the simplest ones, which are connected to the solution of Laplace equation in Feynman classical books and Lectures. Feynman was upset looking in his derived solutions, which have a fictitious singular behavior at the origin. We show how these inconsistencies can be avoided.