索末菲量子化条件修正式的研究

Study on the revised form of Sommerfeld quantization condition

首先说明了波尔量子化条件、普朗克量子化条件与索末菲量子化条件具有对等性;然后对近年来在计算谐振子零点能时提出的索末菲量子化条件修正表达式进行了分析,指出其与波尔氢原子理论存在矛盾;最后在驻波条件的启发下对索末菲量子化条件给出了另外一种修正式,计算表明这一新的修正式既可以正确地给出谐振子的零点能,又能与波尔氢原子理论具有一致性.

It was shown that Sommerfeld quantization condition,Plank quantization condition and Bohr quantization condition were equivalent;then,an analysis was made on the revised form of Sommerfeld quantization which was adopted to solve zero-point energy of the harmonic oscillator in recent years,and the contradiction between this form and the Bohr’s theory of the hydrogen atom was also illustrated;lastly,inspired by the condition of standing wave,an other revised form of Sommerfeld quantization condition was proposed,and the result shows that it can not only gives the zero-point energy of harmonic oscillator,but also be consistent with the Bohr’s theory of the hydrogen atom.