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

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,1 or with the stipulation that, during a spin-flip transition, the orbital radius remains intact.(2) 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,(2) 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 Schrodinger's equation, for Darwin's term, and for the correct 1/2 factor in the spin-orbit coupling energy.