Blasiak, P.; Penson, K.A. and Solomon, A.I.
The Boson normal ordering problem and generalized Bell numbers.
Annals of Combinatorics, 7(2) pp. 127–139.
For any function F(x) having a Taylor expansion we solve the boson normal ordering problem for , with r, s positive integers, , i.e., we provide exact and explicit expressions for its normal form = , where in all a's are to the right. The solution involves integer sequences of numbers which, for , are generalizations of the conventional Bell and Stirling numbers whose values they assume for . A complete theory of such generalized combinatorial numbers is given including closed-form expressions (extended Dobinski-type formulas), recursion relations and generating functions. These last are special expectation values in boson coherent states.
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||boson normal order; Bell numbers; Stirling numbers; coherent states
||Science > Physical Sciences
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||11 Aug 2006
||28 Mar 2014 12:39
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