Logarithmic Terms in the Wave Functions of the Ground State of Two-Electron Atoms

Abstract

A variational calculation for the ground state of two-electron atoms is carried out with a function containing the nonconventional terms $\mathrm{ln}({r}_{1}+{r}_{2})$, ${[\mathrm{ln}({r}_{1}+{r}_{2})]}^{2}$, and ${({{r}_{1}}^{2}+{{r}_{2}}^{2})}^{\frac{1}{2}}$. The convergence of the energy eigenvalues is very good, lending support to the existence of the logarithmic terms in the exact solution of the wave equation.