A quantum-mechanical central limit theorem
- 1 September 1971
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 8 (3) , 454-469
- https://doi.org/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 (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.Keywords
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