Comment on “On the classical analysis of spin-orbit coupling in hydrogenlike atoms,” by A. L. Kholmetskii, O. V. Missevitch, and T. Yarman [Am. J. Phys. 78 (4), 428–432 (2010)] Available to Purchase

Kholmetskii, Missevitch, and Yarman¹ recently reanalyzed the usual classical derivation of spin-orbit coupling in hydrogenlike atoms and found a result “in qualitative agreement with the solution of the Dirac–Coulomb equation for hydrogenlike atoms.” However, their result is based on an equation of translational motion of the electron² that omits any contribution due to the existence of the “hidden” momentum of the electron intrinsic magnetic dipole moment in the electric field of the nucleus. Accounting for hidden momentum is necessary to obtain conservation of linear momentum in the interaction of a classical current-loop magnetic dipole with a point charge.^3–5 Classical electrodynamics textbooks^6,7 recognize this need. It also has been argued⁸ that the hidden momentum of the electron intrinsic magnetic moment must be incorporated in the laboratory-frame analysis of atomic spin-orbit coupling to obtain an equation of motion of the electron polarization that is consistent between the...