The hydrogen atom according to relativistic wave mechanics -- amplitude functions and circulating electronic currents

TL;DR

This paper solves Dirac's equation for the hydrogen atom, revealing detailed amplitude functions and circulating currents that match experimental magnetic moments, advancing relativistic quantum descriptions.

Contribution

It provides explicit amplitude functions and current distributions for hydrogen atom states within relativistic wave mechanics, aligning theoretical predictions with experimental magnetic moments.

Findings

Amplitude functions with four components for each state

Circulating electronic currents produce magnetic dipole moments

Theoretical results agree with experimental magnetic moments

Abstract

The solution of Dirac's equation for the hydrogen atom according to relativistic wave mechanics yields for each state a vectorial amplitude function with four components, two large and two small. Each such component has its characteristic surface of constant amplitude, of which we plot several examples. For each state of the hydrogen atom there is both a density of electronic charge surrounding the atomic nucleus and an electronic current circulating about the polar axis; the latter generates a magnetic dipolar moment that agrees precisely with experiment.