Schrodinger-like equation for the relativistic few-electron atom

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Abstract
The equation for the determination of the energy levels and wavefunctions of quasidegenerate states of the relativistic few-electron atom in the form of the usual eigenvalue problem for an energy operator ('Schrodinger-like equation') is constructed consistently from quantum electrodynamics (QED). Two choices of the space Omega , in which the constructed energy operator H acts, are considered. In the first case Omega = Omega a is the space of the fine structure levels. In the second case Omega = Omega b is the space of all the positive energy states which correspond to the non-relativistic region of the spectrum. The construction of H in the Feynman gauge in the first and second (with the precision up to the terms a2(aZ)2m) orders in a is demonstrated for both choices of Omega . An effective expression for the energy operator Heff, which gives the energy values within am for high Z and within a2(aZ)2m for low Z, is proposed.