Numerical calculation of the ground state of Helium atom using Hyllerass algorithm

Abstract

Hylleraas did the calculation of the ground state in 1926 using the variational parameter a. In this paper we trace Hylleraas historic calculation, the use of computer enables us to improve the approximation found by Hylleraas . The program was written in FORTRAN language, designed in such away that for a particular value of dimension D, we varied the variational parameter α and the corresponding minimum energy was computed. The optimal value of the dimension D, that is D =20, and for all possible values of the basis state, the variational parameter α=1.05 has the lowest energy of –79.015104eV; compared with the historic calculation of Hylleraas the difference is only 0.0329eV. (0.02%).

Journal of the Nigerian Association of Mathematical Physics, Volume 15 (November, 2009), pp 305 - 310