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Journal Article

A Quantum-Mechanical Central Limit Theorem

C. D. Cushen and R. L. Hudson
Journal of Applied Probability
Vol. 8, No. 3 (Sep., 1971), pp. 454-469
DOI: 10.2307/3212170
Stable URL: http://www.jstor.org/stable/3212170
Page Count: 16
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A Quantum-Mechanical Central Limit Theorem
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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 p̄n = n-1/2(p1 + ⋯ + pn), q̄n = n-1/2(q1 + ⋯ + qn) converges in distribution to a normal limit distribution.

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