Lower Bounds to Eigenvalues of the Schrödinger Equation. II. Application to Helium and Li+

The procedure developed in the preceding paper is used to calculate lower bounds to some of the low‐lying ³S levels of helium and Li⁺. These calculations are the first applications of the partitioning technique to the excited states of atoms. They are made using the manifolds $\mathbf{f}{\mathrm{=t(\epsilon )}}^{\text{−1/2}}\mathrm{(\epsilon -}{\mathcal{H}}_0\mathrm{)\hspace{0.17em}}\mathbf{j}$ and f=t(ε)^−1/2h to construct the inner projection t(ε)′. In the latter case, a truncated reduced resolvent T₀(p) was used to approximate T₀. The effect that these projections have on the curves obtained by plotting the multivalued function ε′₁ as a function of ε for these two cases, is also presented. The results seem to indicate that the use of the former manifold to construct t(ε)′ leads to quite close bounds for the ground states but the projection constructed using the latter manifold is better for treating the excited states. The relationships between this method and other lower bound procedures are discussed.