Manifestation the Hidden Symmetry of Coulomb Problem in the Relativistic Quantum Mechanics from Pauli to Dirac Electron

On the basis of generalization of the theorem about the K-odd operators (K is the well-known Dirac operator) certain linear combination is found, which commutes with the Dirac Hamiltonian for Coulomb field. This operator coincides with the Johnson and Lippmann (J.-L.) operator and is intimately connected to the Laplace-Runge-Lenz (LRL) vector. Our approach guarantees not only derivation of of the J.-L. operator but simultaneously commutativity with the Dirac Hamiltonian follows, which was considered usually as a longtime and tedious task. (author)