旧量子理论的兴衰
Rise and fall of the old quantum theory
摘要：
玻尔和索末菲的旧量子理论被抛弃的原因是错误的。它的矛盾不是由轨道概念引起的，而是由一个心理障碍引起的--电子可能与原子核相撞的不可思议。消除这个障碍解决了理论的主要故障-不正确的轨道动量，He原子，H2+分子离子。包含了电子通过原子核的振荡--一个被称为“库仑振荡器”的概念--使得旧的量子理论与量子力学一致（尽管缺乏波动特征）。玻尔-索末菲模型的三重成功在于它对氢原子（和单电子离子）的正确描述，涉及：（1）能级Enl，（2）轨道角动量Lnl--如果修正为Lnl ^2 = 1（1 +1）hbar ^2并包括库仑振子的话--以及（3）轨道的空间量子化--（Lnl）z = ml hbar。这些成就简洁地表示为主要的，角和磁量子数（n，l，ml）和可视化的轨道椭圆几何形状-主轴，顶点曲率和倾斜角，分别。轨道几何形状也是平均轨道大小的原因。此外，库仑振子提供了一个自然的解释（各向同性）超精细相互作用。旧量子理论的缺点在于忽视了粒子的三个性质--自旋、波性和量子统计。尽管存在这些缺陷，玻尔-索末菲模型的视觉吸引力仍然是一种教学资产，以补充量子力学的抽象特征。
英文摘要：
The old quantum theory of Bohr and Sommerfeld was abandonned for the wrong reason. Its contradictions were caused not by the orbit concept but by a mental barrier--the inconceivability that an electron might collide with the atomic nucleus. Removing that barrier resolves the theory's main failures--incorrect orbital momenta, He atom, H2+ molecule ion. The inclusion of electron oscillations through the nucleus--a concept called "Coulomb oscillator"--renders the old quantum theory consistent with quantum mechanics (although devoid of wave character). The triple success of the Bohr-Sommerfeld model is its correct description of the H atom (and one-electron ions) concerning (1) the energy levels Enl, (2) the orbital angular momenta Lnl--if corrected as Lnl^2 = l(l+1) hbar^2 and with the Coulomb oscillator included--and (3) the orbits' space quantization--with (Lnl)z = ml hbar. These achievements are succinctly represented by the principal, angular and magnetic quantum numbers (n, l, ml) and visualized by orbital ellipse geometry--major axis, vertex curvature, and tilt angle, respectively. Orbit geometry also accounts for the average orbit size. Moreover, the Coulomb oscillator provides a natural explanation of (isotropic) hyperfine interaction. The shortcomings of the old quantum theory lie in its neglect of three properties of particles--their spin, their wave nature and their quantum statistics. These deficiencies notwithstanding, the visual appeal of the Bohr-Sommerfeld model remains a pedagogical asset to complement the abstract character of quantum mechanics.
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