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Combinatorics and Boson normal ordering: A gentle introduction

Blasiak, Pawel; Horzela, Andrzej; Penson, Karol A.; Solomon, Allan I. and Duchamp, Gerard H.E. (2007). Combinatorics and Boson normal ordering: A gentle introduction. American Journal of Physics, 75(7) pp. 639–646.

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We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling numbers enumerating partitions of a set. This framework reveals several inherent relations between ordering problems and combinatorial objects, and displays the analytical background to Wick's theorem. The methodology can be straightforwardly generalized from the simple example we discuss to a wide class of operators.

Item Type: Journal Article
ISSN: 0002-9505
Keywords: normal order;bosons; quantum mechanics; combinatorics
Academic Unit/Department: Science > Physical Sciences
Item ID: 7397
Depositing User: Allan Solomon
Date Deposited: 06 Jul 2007
Last Modified: 02 Dec 2010 19:58
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