The WKB method for the Dirac equation with the vector and scalar potentials

Abstract

The WKB approximation is developed for the Dirac equation with the spherically symmetrical vector and scalar potentials. The relativistic wavefunctions are constructed, new quantization rule containing the spin-orbital interaction is obtained. For spherically symmetrical model of the Stark effect the quasi-classical spectrum of relativistic hydrogenlike atom is calculated. Application of the WKB method to the mass spectrum of the hydrogen-like quark systems was done.