The (2s)²¹S State Solution of the Non-relativistic Schr dinger Equation for Helium and the Negative Hydrogen Ion

Abstract

A finite set of possible Slater determinants with spatial part constructed from an orthonormal complete one-electron set of associated Laguerre functions in the radial coordinates, and Legendre functions in the angular coordinates, has been introduced into the minimal sequence of the Ritz variational principle applied to the (2s)2 state solution (L = 0) of the two-electron wave equation for infinite nuclear mass. The sequence converges on a certain limiting eigen-function of the energy state. The numerical solution of the function and the corresponding energy value are given for helium as well as the negative hydrogen ion. The identification of certain helium lines in the vacuum ultra-violet is discussed.