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 $\ln (r_1+r_2)$, ${\left[\ln \right(r_1+r_2\left)\right]}^2$, 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.