The Boson normal ordering problem and generalized Bell numbers

Blasiak, P.; Penson, K.A. and Solomon, A.I. (2003). The Boson normal ordering problem and generalized Bell numbers. Annals of Combinatorics, 7(2) pp. 127–139.

DOI (Digital Object Identifier) Link:	http://dx.doi.org/doi:10.1007/s00026-003-0177-z
Google Scholar:	Look up in Google Scholar

Abstract

For any function F(x) having a Taylor expansion we solve the boson normal ordering problem for $F[(a^\dag)^ra^s]$ , with r,s positive integers, $F [(a, a^\dag]=1$ , i.e., we provide exact and explicit expressions for its normal form $\mathcal{N} \{F[(a^\dag)^ra^s]\} = F[(a^\dag)^ra^s]$ , where in $\mathcal{N}(F)$ all a's are to the right. The solution involves integer sequences of numbers which, for $r,s\geq 1$ , are generalizations of the conventional Bell and Stirling numbers whose values they assume for $r=s=1$ . 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.

Item Type:	Journal Article
ISSN:	0218-0006
Extra Information:	Some of the symbols may not have transferred correctly into this bibliographic record.
Keywords:	boson normal order; Bell numbers; Stirling numbers; coherent states
Academic Unit/Department:	Science > Physical Sciences
Item ID:	4891
Depositing User:	Users 6041 not found.
Date Deposited:	11 Aug 2006
Last Modified:	02 Dec 2010 19:52
URI:	http://oro.open.ac.uk/id/eprint/4891

Actions (login may be required)

	View Item
	Report issue / request change

Policies | Disclaimer