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 schrodinger equation. It is simple to solve the problem by using Runge-Lenz vector.