The calculation is short and neat.
Stefan can you properly introduce all variables you use? "e" in physics can be an electron or a variable "de" means nothing unless until you define the meaning of "d" e.g. as derivation... the use teh proper letter. Also "x" without index is meant as vector?
All these classic (Dirac, Schrödinger Klein-Gordon) equation fail do describe Hydrogen in detail, because the topology used is a sphere not a torus. So it always will be, as GUT-CP too, just a first order approximation.