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.

本工作探讨了E. A. 希勒拉斯（E. A. Hylleraas）在1928至1930年间提出的双电子原子量子力学问题。希勒拉斯通过将电子间的坐标作为该问题的独立变量，在波函数（wavefunction）中引入了显式关联，该方法可获得精度极高的能量计算结果。如原始研究所示，本文针对1、2、3及6个基函数（basis functions）的场景给出了该问题的求解过程；此外还采用140个基函数开展求解，结果表明双电子原子的能量可被计算至7位有效数字。本文所呈现的数值方法可供本科阶段学生学习使用。