Self-consistent one-electron equation for many-electron systems and its general application to ground and excited states

The present status of ab initio calculations for electronic states requires the further development of the quantum many-body theory which mainly targets the improvement of the fundamental equation in the sense of completely non-empirical, i.e., true ab initio theory. In compliance with this requirement, we present an alternative self-consistent one-electron equation different from both the Hartree-Fock equation and the Kohn-Sham equation, but essentially the improvement and unification of them. This equation includes the exchange and correlation effect in an ab initio way based on the quantum principles. To derive a one-electron equation including the exchange effect in an explicit way in terms of antisymmetric wavefunctions, we introduce a new concept called the equivalent function. Moreover, to treat the electronic correlation in a first-principle way, we introduce another new concept referred to as the phase norm which specifies the mutual-electron-approachable limit in terms of phase space. The derived equation becomes a self-consistent one-electron equation which satisfies the main requirements for ab initio calculations. This equation offers a big advantage of calculating electronic states of many-electron systems in a unified way commonly applicable to all stationary state problems, irrespective of ground or excited states, without recourse to the approaches based on the Hartree-Fock or the density functional theory.