  This report presents the analytical solution of the Schrodinger equation and
its corresponding wave function for the neutral helium or helium-like atoms in
the ground state. The state functions of the two electrons for s=0 and l=0 as
well as their boundary conditions are examined in detail. Furthermore, a method
for describing a generic electron potential consisting of Coulomb and exchange
interactions is derived, and the resulting potential function is integrated
into the Schrodinger equation as a potential term. In addition, the altered
electromagnetic coupling of the electrons due to vacuum polarization effects is
investigated and finally the Schrodinger equation for the neutral 1S0 Helium,
historically known as Para-Helium, is solved using Laplace transformations. The
energy in the ground state is then determined, and it can be shown that this
agrees with the literature values given the fact that the electron can be
assumed to be a point-like particle. In the context of these investigations, an
upper limit estimation for the spatial dimension of the electron can also be
given as well is the existence of a minimal distance of a stable bonding state
between two electrons, which can be interpreted as an entangled state; in
addition, the chemical inertness of helium with regard to chemical reactions -
i.e. the principle of the "closed" electron shell - can be made plausible by
the quantum mechanical electron configuration and its consequences with regard
to binding energy. The wave function found for the helium atom is compared with
the known solutions for the hydrogen atom, and essential differences between
the two are worked out.
