SCHRODINGER-LIKE EQUATION FER THE RELATIVISTIC FEW-ELECTRON ATOM

The equation for the determination of the energy levels and wavefuncti ons of quasidegenerate states of the relativistic few-electron atom in the form of the usual eigenvalue problem for an energy operator ('Sch rodinger-like equation') is constructed consistently from quantum elec trodynamics (QED). Two choices of the space Omega, in which the constr ucted energy operator H acts, are considered. In the first case Omega = Omega(a) is the space of the fine structure levels. In the second ca se Omega = Omega(b) is the space of all the positive energy states whi ch correspond to the non-relativistic region of the spectrum. The cons truction of H in the Feynman gauge in the first and second (with the p recision up to the terms alpha(2)(alpha Z)(2)m) orders in alpha is dem onstrated for both choices of Omega. An effective expression for the e nergy operator H-eff, which gives the energy values within alpha m for high Z and within alpha(2)(alpha Z)(2)m for low Z, is proposed.