概率性经典粒子的量子可观测量
Quantum observables for probabilistic classical particles
AI总结：
研究针对微观物理中概率性经典粒子，提出用更稳健的量子可观测量，通过刘维尔方程的量子形式体系探讨，展示量子系统如何从经典统计中产生，还研究了特殊势下子系统及双缝实验干涉等，守恒可观测量或与尘埃、行星动力学有关。
AI中文摘要：
经典的位置和动量可观测量并不适用于微观物理情形中的粒子，其典型概率分布具有显著的离散性。我们提议为概率性经典粒子使用更稳健的量子可观测量。这些量子可观测量是统计可观测量，对于给定的经典位置和动量并不取固定值。在经典统计的量子形式体系中讨论了刘维尔方程的解。统计可观测量由非对易算符表示。这些可观测量没有定义经典关联函数，贝尔不等式也不适用。我们针对一般势展示了量子系统如何从经典统计中出现。对于谐振子势和库仑势的特殊情况，我们研究了描述量子粒子所有特征的子系统，涵盖了氢原子和量子谐振子的离散能谱。我们还讨论了双缝实验的干涉。守恒的统计可观测量可能也与尘埃或行星的概率动力学相关。
英文摘要：
The classical observables of position and momentum are not well adapted to particles in a microphysical situation where typical probability distributions are characterized by a substantial dispersion. We propose the use of more robust quantum observables for probabilistic classical particles. The quantum observables are statistical observables which do not take fixed values for a given classical position and momentum. Solutions of the Liouville equation are discussed in the quantum formalism for classical statistics. Statistical observables are represented by non-commuting operators. No classical correlation function is defined for these observables and Bell's inequalities do not apply. We demonstrate for a general potential how a quantum system emerges from classical statistics. For the particular cases of a harmonic potential and a Coulomb potential we investigate subsystems which describe all features of a quantum particle. This covers the discrete energy spectrum of the hydrogen atom and quantum harmonic oscillator. We discuss the interference for the double-slit experiment. Conserved statistical observables may also be relevant for the probabilistic dynamics of dust or planets.
