Finite‐element calculations for the helium atom

Abstract

Abstract We give the explicit form of the Hylleraas–Breit transform in the current paper and apply it to fixed‐nucleus problems of heliumlike ions. Employing the relation between the total angular momentum and the Hamilton, the six‐dimensional Schrödinger equation is transferred into three‐dimensional systems of equations. We use the Lagrange finite‐element method to obtain numerical solutions for some low‐lying S , 1 s 2 p 3 P , and 1 s 3 d 3 D states of the helium atom. The relative errors of our approximate energies are: O (10 −8 ) a.u. for S states, O (10 −7 ) a.u. for 1 s 2 p 3 P state and O (10 −5 ) a.u. for 1 s 3 d 3 D state. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004