Helium Wave Equation

Abstract

The wave function for the ground state of helium has been obtained by a method which involves iterating in one direction only, the values of the function in any one plane being made mutually consistent by solving 30 simultaneous equations in 30 unknowns. The local energy value $\frac{(H\ensuremath{\varphi})}{\ensuremath{\varphi}}$ is approximately constant over most of space, the maximum deviations occurring at large distances between electron and nucleus. The present accuracy is not sufficient to give a good determination of the eigenvalue, but it appears to be at least within 0.5 percent of the experimental value.