Man'ko Margarita A, Man'ko Vladimir I
Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia.
Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow 141700, Russia.
Entropy (Basel). 2023 Jan 22;25(2):213. doi: 10.3390/e25020213.
A short review constructing the probability representation of quantum mechanics is given, and examples of the probability distributions describing the states of quantum oscillator at temperature and the evolution of quantum states of a charged particle moving in the electric field of an electrical capacitor are considered. Explicit forms of time-dependent integrals of motion, linear in the position and momentum, are used to obtain varying probability distributions describing the evolving states of the charged particle. Entropies corresponding to the probability distributions of initial coherent states of the charged particle are discussed. The relation of the Feynman path integral to the probability representation of quantum mechanics is established.
给出了构建量子力学概率表示的简短综述，并考虑了描述温度下量子振子状态以及在电容器电场中运动的带电粒子量子态演化的概率分布示例。利用在位置和动量上呈线性的含时运动积分的显式形式，来获得描述带电粒子演化状态的变化概率分布。讨论了与带电粒子初始相干态概率分布相对应的熵。建立了费曼路径积分与量子力学概率表示的关系。
