观念. 量子化 [量子化]
观念. 量子化 [量子化]
量子化最早是指经典力学系统到量子力学系统的某种转变. 与范畴化类似, 量子化不是自然的, 确定的过程, 而是一种 “艺术”.
- 经典力学的可观测量是相互交换的, 而量子力学系统的可观测量不交换;
- 量子化所得的系统往往带有一个参数, 记作 $q$ 或 $h$ ($\hbar$), 这些参数的极限情形往往对应着经典力学系统.
后来, 人们用量子化指代具有上述特征的更广泛的现象.
力学系统
Since the observables in classical mechanics form a Lie algebra under Poisson bracket, what then is the corresponding Lie group? The answer to this is of course “well known” in the literature, in the sense that there are relevant monographs which state the answer. But, maybe surprisingly, the answer to this question is not (at time of this writing) a widely advertized fact that has found its way into the basic educational textbooks. The answer is that this Lie group which integrates the Poisson bracket is the “quantomorphism group”, an object that seamlessly leads to the quantum mechanics of the system.