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A quantum-mechanical central limit theorem

Published online by Cambridge University Press:  14 July 2016

C. D. Cushen  and
R. L. Hudson
C. D. Cushen
Affiliation:
University of Nottingham
R. L. Hudson
Affiliation:
University of Nottingham
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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 (pn, qn), 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.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 3 , September 1971 , pp. 454 - 469
Copyright
Copyright © Applied Probability Trust 1971 

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