ABSTRACT
The wave equation for the helium atom in a state with vanishing angular momentum was first deduced by E. Hylleraas in his classical papers on the ground state of helium [1]. This equation shall be referred to, for the sake of brevity, as the Hylleraas equation. The Hylleraas equation corresponds to a mechanical system with three degrees of freedom; it is natural to take as independent variables the two distances of the electrons from the nucleus and the angle between their radii-vectors. To simplify calculations connected with the Ritz method, Hylleraas took as independent variables the three distances; the wave function to be varied was expanded in a power series of the three distances. Careful calculations made by Hylleraas showed a good agreement with the experimental values of the energy levels. It has been pointed out, however [2], that the exact solution of the Hylleraas equation does not possess an expansion of the supposed type, and the true form of the expansion was still to be found.
