Status of the Radial Schrodinger Equation

TL;DR

This paper examines the conditions under which the traditional radial Schrödinger equation aligns with the full Schrödinger equation, revealing a necessary boundary condition at the origin.

Contribution

It identifies a specific boundary condition required for the traditional radial Schrödinger equation to be consistent with the full equation.

Findings

Traditional radial Schrödinger equation requires a boundary condition at the origin.

Compatibility with the full Schrödinger equation depends on an additional constraint.

Discussion of implications for quantum mechanical boundary conditions.

Abstract

We show that equation for radial wave function in its traditional form is compatible with the full Schrodinger equation if and only if a definite additional constraint required. This constraint has a boundary condition form at the origin. Some of consequences are also discussed.