On Urn Models, Non-commutativity and Operator Normal Forms

Details On Urn Models, Non-commutativity and Operator Normal Forms On Urn Models, Non-commutativity and Operator Normal Forms

2010-10-12

arxiv.org/abs/1010.2445v1

Phys. Lett. A 374, 4808-4813 (2010)

Physics

Quantum Physics

7 pages, 2 figures

Scientific paper

10.1016/j.physleta.2010.10.003

Non-commutativity is ubiquitous in mathematical modeling of reality and in many cases same algebraic structures are implemented in different situations. Here we consider the canonical commutation relation of quantum theory and discuss a simple urn model of the latter. It is shown that enumeration of urn histories provides a faithful realization of the Heisenberg-Weyl algebra. Drawing on this analogy we demonstrate how the operator normal forms facilitate counting of histories via generating functions, which in turn yields an intuitive combinatorial picture of the ordering procedure itself.

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