Relativistic Corrections to the Energy of the Electron in a Hydrogenlike Atom

Abstract

Using the previously found solution of the Dirac equation for an electron in the field of the nucleus (Ze), expressed in terms of the eigenfunction of the spin projection operator Σ₃, in the expansion in the small parameter (Zα), α = е²/ħс ≈ 1/137, relativistic and spin-orbit corrections to the energy of the electron in a hydrogenlike atom are calculated, where the latter, in our view, are represented in an easier to visualize form in comparison with previously known classical results. This work may be of methodological interest in the sense of some modification of the corresponding sections of the traditional course on quantum mechanics.