Some results for the wave function at the origin for S-wave levels

TL;DR

This paper analyzes how the wave function at the origin for S-wave levels depends on quantum numbers and mass, providing specific results for potentials with certain curvature properties.

Contribution

It offers new analytical results for the dependence of the S-wave radial wavefunction at the origin on quantum number and reduced mass for specific potentials.

Findings

Derived formulas for $R_{n0}(0)$ dependence on $n$ and $bc$

Results applicable to potentials with definite curvature

Enhanced understanding of wave function behavior at the origin

Abstract

Starting with the $S$-wave radial equation for an attractive central potential $V(r)$, we give results for the $n$ (principal quantum number) and the $\mu$ (reduced mass) dependence of $R_{n0}(0)$, the $S$-wave radial wavefunction at the origin, for potentials with definite curvature.