The Helium Wave Equation

This paper is a sequel to the preceding one by Gronwall. In Part I it is shown that the ground state eigenfunction, if it exists, cannot have the form ψ=Σp,k=0^∞s^p+γap, k(β)coskφ, where s=r1/2=(r₁^_²+r₂^_²)1/2, and γ is some constant. In Part II, it is assumed that the solution of Gronwall's infinite system of ordinary differential equations (see preceding abstract) is to be found by extrapolation from a finite system. Arguments are given to show that if the wave function is finite everywhere except at the origin, then the expansion about the origin is of the form ψ=Σk=0^∞c⁽ᵏ⁾(s,β,φ)(logs)ᵏ, where the c⁽ᵏ⁾'s are ascending power series in s.