With a pedagogical aim suited for the upper-division undergraduate, we apply the old quantum theory (pre-Schrdinger) to the study of many-electron atomic species. We eschew the typical picture with circular atomic Bohr orbits of non-zero angular momentum and instead consider the electrons to be ‘bouncing’ along straight lines on the nucleus. Abandoning the circular orbits of Bohr comes at the cost of a meanfield approximation but at the gain of a physically correct (vanishing) electron angular momentum for the first four elements. The Bohr–Sommerfeld meanfield (or perturbation) calculations, of which we present a variety of increasing numerical complexity, generally give results accurate to within a few percent. For He, also excited states are calculated and these results quickly converge on the exact values already for the first excited state. The main source of error in the semiclassical calculation with respect to the exact results is traced to the neglect of the Pauli principle, since it is virtually present only for the singlet ground-state but not the lowest triplet state.

出于适合高年级本科生的教学目标，我们将旧的量子理论（薛定谔之前）应用于多电子原子种类的研究。我们避开了具有非零角动量的圆形原子玻尔轨道的典型图片，而是考虑电子沿着原子核上的直线“弹跳”。放弃玻尔的圆形轨道以平均场近似为代价，但前四个元素的物理正确（消失）电子角动量的增益。Bohr-Sommerfeld 平均场（或扰动）计算，我们提出了各种增加的数值复杂性，通常给出的结果精确到几个百分点。对于 He，还计算了激发态，并且这些结果很快收敛到第一个激发态的精确值。