Theory of atomic hyperfine structure

The new equation for 1/2 spin relativistic particle is proposed. In comparison with Dirac equation the proposed equation (i) is completely symmetric with respect to particle and its antiparticle, (ii) predicts the hyperfine structure of electron energy levels in Coulomb field of nucleus with zero magnetic moment, (iii) explains the Lamb shift and electron anomalous magnetic moment without secondary quantization either the matter or the radiation field. The analytically tractable solutions of the proposed equation are found for the problems of electron motion in the Coulomb field, in uniform magnetic field and in superposition of Coulomb and uniform magnetic fields.