Dirac equation for the electron in an external field

The noncovariant form of the Dirac equation for an electron in an external field is  

Here p = —iV is the electron momentum operator, d, P are the standard Dirac matrices, A is the vector potential and V is the scalar potential of the external field. The wave function (r,t) is the four-component spinor. For the stationary state  

Here E, are the Dirac eigenvalues, index s runs over the complete spectrum of the Dirac Hamiltonian. This spectrum includes the solutions with positive and negative energy values E,. For the bound-state solutions the 

The introduction of the Dirac - conjugated wave function (x) = 74 leads to the equation  

The negative-energy Dirac states within QED are interpreted with the help of the charge conjugation transformation  

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