Spin-orbit coupling in the hydrogen atom, the Thomas precession, and the exact solution of Dirac's equation

TL;DR

This paper discusses the limitations of Bohr's model in explaining hydrogen atom spin phenomena and emphasizes the importance of Dirac's equation for accurate physical understanding of spin-orbit interactions.

Contribution

It highlights the inadequacy of Bohr's model for spin-orbit coupling and advocates for the use of Dirac's equation to accurately describe atomic spin effects.

Findings

Bohr's model cannot fully explain spin-orbit interaction.

Dirac's equation provides a comprehensive understanding of spin-related phenomena.

The Thomas precession hypothesis is questionable and not necessary with Dirac's framework.

Abstract

Bohr's model of the hydrogen atom can be extended to account for the observed spin-orbit interaction, either with the introduction of the Thomas precession, or with the stipulation that, during a spin-flip transition, the orbital radius remains intact. In other words, if there is a desire to extend Bohr's model to accommodate the spin of the electron, then experimental observations mandate the existence of the Thomas precession, which is a questionable hypothesis, or the existence of artificially robust orbits during spin-flip transitions. This is tantamount to admitting that Bohr's model, which is a poor man's way of understanding the hydrogen atom, is of limited value, and that one should really rely on Dirac's equation for the physical meaning of spin, for the mechanism that gives rise to the gyromagnetic coefficient g=2, for Zeeman splitting, for relativistic corrections to Schr\"odinger's equation, for Darwin's term, and for the correct 1/2 factor in the spin-orbit coupling energy.