A quantum-mechanical central limit theorem

1971/09/01 by C. D. Cushen, R. L. Hudson · 10 citations
Physics and Astronomy · Computer Science · #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #Quantum Information and Cryptography

paper · doi:10.2307/3212170

Abstract

The concepts of distribution operator, stochastic independence, convergence in distribution and normal distribution are formulated for pairs of canonically conjugate quantum-mechanical momentum and position operators. It is shown that if the sequence ( p n , q n ), n = 1, 2, ··· is stochastically independent and identically distributed with finite covariance and zero mean then the sequence of pairs of canonical observables converges in distribution to a normal limit distribution.

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