The semiclassical two-electron atom and the old quantum theory

Abstract

The semiclassical equivalent of the Hylleraas variational method for helium is obtained and applied to the two-electron atom. The accuracy is comparable to the early quantal results of Hylleraas and Eckart. The failure of the old quantum theory to obtain an accurate energy is explained as an omission of zero-point motion through half-integer quantum numbers and the lack of a variational method to obtain an adequate model, and not to any intrinsic fault of the theory. The results suggest that semiclassical variational methods will assist in the study of resonance states and of planetary atoms.