CONTINUOUS REPRESENTATIONS IN THE STATISTICAL THEORY OF ELECTRONIC ENERGIES

Author Institution: Brandeis University; Tufts University“An investigation of alternative bases of representation has been conducted for the hydrogen atom in order to remove singularities in charge densities at nuclei associated with Thomas-Fermi theory. The result is a generalized Thomas-Fermi that includes the usual one as a special case. The Hamiltonian H was partitioned into $H_{o} + H’$, and a basis defined by $H_{o} \Psi_{k} = E^{o}_{k} \Psi_{k}$. The treatment, leads to an expression for the single particle density that reduces to the Thomas-Fermi density in the limiting case. The energy of the H-atom calculated in this way shows a notable improvement over that calculated from Thomas-Fermi theory.