On Perturbative SOC methods

For a 1s electron, whose velocity is equal to Z in atomic units, the relativistic effect leading to heavier mass, for heavy elements (Z high), thus cannot be ignored. The result is a relativistic contraction of the orbitals, causing lowering of Zeff on orbitals of higher angular momentum. This calls for a relativistic treatment of quantum dynamics. For an equation of motion to hold in a relativistic treatment, it must be Lorentz invariant, i.e, it must be invariant under a Lorentz transformation between space and time co-ordinates. Clearly, the Schroedinger equation contains different space and time derivatives, and so is not Lorentz invariant.