论各向同性谐振子能级的又一求解方法

在经典力学中的中心力场中,除了能量 E 和角动量 L 两个运动积分外,还存在着第三个运动积分,即 Runge-Lenz 矢量,该矢量可算符化。以各向同性谐振子为例,运用 Runge-Lenz 矢量简洁地求解出量子力学中另一类典型问题——谐振子的能级公式,与求解薛定谔方程的结果一致,从中可看出用 Runge-Lenz 矢量处理问题的简洁性。

Another Solution to Energy Level of Isotropic Oscilla

In classical mechanic,besides the two integrals energy E and angular momentum L in the centre of force field, there exists a third integral,Runge-Lenz vector which can be operated.This article cites the isotropic oscilla as an example.By using Runge-Lenz vector,the result of energy level formular of oscilla is the same with sehrodinger equation.It is simple to solve the problem by using Runge-Lenz vector.