What is the boundary condition for radial wave function of the Schrödinger equation ?

Abstract

There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin, particularly for singular potentials. A careful derivation of the radial Schrödinger equation leads to the appearance of a delta function term when the Laplace operator is written in spherical coordinates. As a result, regardless of the behavior of the potential, an additional constraint is imposed on the radial wave function in the form of a vanishing boundary condition at the origin.

15 pages

References in corpus (2)

• Electron Capture and Scaling Anomaly in Polar Molecules
• Some Problems of Self-Adjoint Extension in the Schrodinger equation

Cited by in corpus (3)

• 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
• Magnetic States at Short Distances
• Solutions of the Schrödinger equation, boundary condition at the origin, and theory of distributions