玻尔-索末菲的椭圆轨道理论的推导

Derivation of Bohr-Sommerfeld elliptic orbit theory

本文从椭圆运动的轨道方程出发,结合量子化条件,详细推导了玻尔-索末菲的椭圆轨道的理论,给出了电子的能量以及量子化的半长轴a和半短轴b的表达式。能级公式与玻尔通过对圆轨道得到的结果一致,即能量是量子化的。而电子具有一定能量时,可能的状态n种,即n重简并。

Starting from the orbital equations of elliptical motion and combining with the quantization conditions,the theory of elliptic orbitals of Bohr-Sommerfeld is deduced in detail.The energies of the electron and the quantized half-and semi-minor axes b expression.The energy level formula is consistent with the result Bohr obtained for a circular orbit,that is,the energy is quantized.And electronic has a certain energy,the possible state n species,that is,n heavy degenerate.