Hydrogenic ground state energy, variational treatment

The Bohr model gave the correct energies for the hydrogen atom but failed when applied to helium. Hence, in the early days of quantum mechanics, it was important to show that the new theory could give an accurate treatment of helium. The pioneering work on the helium ground state was done by Hylleraas in the years 192 1930. To allow for the effect of one electron on the motion of the other, Hylleraas used variational functions that contained the interelectronic distance ri2- One function he used is... 

Calculations based on the continuum dielectric model have been performed by the hydrated electron in the limit of zero cavity size (19). The general treatment is based on a variational calculation using hydrogenic type wave functions for the ground and the first excited states. This treatment is based on a Hartree Fock scheme, where the Coulomb and exchange interaction of the excess electron with the medium are replaced by the polarization energy of a continuous dielectric. The results obtained are summarized in Table V. The fair agreement obtained with... 

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