仿激光开系的阻尼振子量子化方案

QUANTUM THEORY OF A DAMPED HARMONIC OSCILLATOR SIMULATING LASER OPEN SYSTEM

激光全量子理论对激光开系采用热浴模型进行了量子化。近两年来,文献[1,2]又报道了两种阻尼振子的量子化方案,与激光开系热浴模型比较,迥然不同。本文在简要介绍激光开系热浴模型后,便与文献[1,2]方案进行分析比较,指出这后两种方案存在的困难,并提出仿激光开系的阻尼振子量子化方案。最后求得仿开系方案的Hamiltonian及相应的Schrdinger方程的解及力学量平均值的计算。在量子起伏项不再出现阻尼因子。

We have analysed the quantization schemes presented in references [1, 2] for a damped harmonic oscillator and found out that there are some defects in volved in these schemes. In order to remedy these defects, we assume the coordinate system fluctuating with a velocity g(t) in addition to damping force f(t) proportional to the velocity and suggest a method of quantization for this system based on the full quantum theory of lasers. It is proved that the usual Heisenberg relation xp梡x=ih can be maintained, but the quantum term in statistical average value of physical variable does not damp as shown in reference [1].