扩展玻尔模型:索末菲早期原子理论,1913–1916

Extending Bohr:Sommerfeld's Early Atomic Theory,1913-1916

本文从阿诺德·索末菲(Arnold Sommerfeld)个人研究日程的角度出发,回顾了索末菲对于玻尔原子模型的反应。他欣赏尼耳斯·玻尔(Niels Bohr)对有关氢元素的里德堡公式的推导,但却对其模型有所批评。1913年,索末菲试图通过扩展亨德里克·洛伦兹(Hendrik Lorentz)关于塞曼效应的经典理论来解释近期发现的帕邢-贝克效应。光谱线在电场中分裂这一发现,是其研究计划中的另一项挑战。经典理论在这两方面都失败了,因此索末菲转而代之以玻尔模型。通过量子化电子绕原子核的径向运动和方位角,索末菲扩展了玻尔模型。在非相对论情形中,他再次得到了里德堡公式(此时用两个量子数总和来取代玻尔模型中的单个量子数);在相对论情形中,他则得到了后来有名的精细结构公式。虽然关于从玻尔理论到玻尔-索末菲理论的发展一直有详实的历史记载,但从索末菲私人和专业信件往来的角度去考察这一过程中的动力却是一个全新的视角。

Arnold Sommerfeld＇s response to Bohr＇s atomic model is reviewed from the perspective of Sommerfeld＇s personal research agenda. He admired Bohr＇s derivation of the Rydberg formula for hydrogen but was otherwise critical about the model. In 1913, Sommerfeld attempted to explain the recently discovered Paschen-Back-effect by generalizing Lorentz＇s classical theory of the Zeeman effect. The discovery of the splitting of spectral lines in an electric field （Stark effect） entered his agenda as another challenge In both cases the classical approaches finally failed, so that Sommerfeld resorted to Bohr＇s model as an alternative. He extended Bohr＇s model by quantizing both the azimutal and radial motion of the electron around the nucleus. In the non-relativistic case he recovered Bohr＇s Rydberg formula （now with a sum of two quantum numbers instead of a single one as in Bohr＇s model）; in the relativistic case he obtained what became known as the finestructure-formula. Although the development from the Bohrto the Bohr-Sommerfeldtheory has been the subject of detailed historical accounts, the dynamics of this process appears in a new light when described mainly from the perspective of Sommerfeld＇s private and professional correspondence