On the ground state of a model for compressed helium

Abstract

In the problem of the “compressed helium atom”, the boundary condition that the wave function ψ must vanish at infinity (r = ∞), is replaced by: ψ = 0 at a finite r = r0. This problem is solved by a variational method, which for the limiting case of the free atom (r0 → ∞) coincides with one of Hylleraas' approaches to the helium problem. The energy and kinetic energy of the electrons in the ground state are calculated as functions of r0 and the corresponding pressure (§ 5).