A Strong Contradiction in the Conventional Non-relativistic Theory of the ground State Helium Atom and Helium-like Ions

In the conventional theory of the ground state of helium atom, any solution of the two-electron Schr dinger equation is wrong! That is caused by a strong imbalance of proportions of the attraction versus repulsion operators’ acting on a wave function, in the initial differential Schr dinger equation and in its integral algebraic form. In the differential equation, the attraction operators act on the radial part of wave function independently from one another obeying the true proportion: one attraction versus one repulsion per electron. But the resulting wave function turns out to satisfy the wrong integral proportion: two attraction energies versus one repulsion energy per electron. The underlying contradiction is un-coincidence of the additivity rules of energies and energy operators: whereas energies of the electrons may be summed the corresponding energy operators referred to different electrons may not. Consequences of this principal contradiction are discussed.