Variational method for two-electron atoms

The ground-state energies for helium-like atoms are computed by the Ritz variational method. The trial wave function is chosen to be of the form ψ=[ln(r12+e)+C(r1−r2)2] ×exp[−S(r1+r2)], where r1 and r2 are the distances of the electrons from the nucleus, r12 the distance between the electrons, e the natural base of logarithms, and the parameters C and S are determined by minimizing the energy of the atom. The numerical results are presented and compared with those of other authors.