量子力学中的Lindeberg-Feller中心极限定理

A Quantum-Mechanical Lindeberg-Feller Central Limit Theorem

本文证明了:若{(P_n,q_n)}_(n-1)~∞是Hilbert空间H上的一列随机独立的典型观察量对,则??依分布收敛到标准正态分布算子.

It is showed in this paper that if the sequence {(p_n, q_n)}_(n=1)~∞ is stochastically independent pairs of canonical observables with finite covariance matrices {Γ^((n))}_(n=1)~∞ and zero means then the sequence of pairs of observables ?? converges in distribution to the standard normal distribution operator.