Three-dimensional statistical reduction of the non-relativstic Schr\"{o}dinger equation for electrons with pair-wise Coulomb interactions

Based on Ritz variational principle, we reduce in statistical fashion the non-relativistic $N$-body Schr\"{o}dinger equation for electrons with Coulomb interactions to a three-dimensional wave-equation for the motion of one electron with the residual $N-1$ electrons acting spectators of its motion [1]. As a consequence the Pauli's exclusion principle is interpreted as dynamical principle. Analytic solutions of the all electron quantal equations for the ground and excited states of the helium and lithium isoelectronic sequences will be represented and the comparison with the experimental measurements for the ground-state ionization potentials of atoms shown. \\[0pt] [1] B.~D.~Obreshkov , Phys.~Rev.~A {\bf 78}, 032503 (2008).