阻尼谐振子的量子力学处理

本文假设量子力学中也允许引入阻尼力的描述,给出对与速度成正比的阻尼系统用正则化变换的处理方法,以一维谐振子为例作了具体计算。结果与经典力学比较表明是合理的。关键词：

QUANTUM MECHANICAL TREATMENT OF A DAMPED HARMONIC OSCILLATOR

Assuming a damping force proportional to the velocity, it is shown that the usual quantum condition between the physical variables, namely the displacement and the momentum, has to be modified by the damping. However, it is possible to change to new variables which are canonical. Then we can apply the usual quantum mechanics and use the usual physical interpretation through the statistical average values. The case of a one-dimensional damped harmonic oscillator under the action of an arbitrary external force has been worked out as an example. No difficulty arises and the results are reasonable.