THE HYLLERAAS METHOD FOR TWO ELECTRONS ATOMS

The quantum mechanics of two electrons atoms, as suggested by E. A. Hylleraas in the period between 1928-1930, is discussed in the present work. Hylleraas introduced explicit correlations in the wavefunction by treating the coordinates between the electrons as an independent variable of the problem, an approach that gives very precise energy values. Solution of the problem is given for one, two, three and six basis functions, as in the original work. The solution is also carried out with 140 basis functions, showing that the energy for two electron atoms can be calculated with seven significant figures. Numerical methods presented here are accessible to undergraduated level students.