The Boson Normal Ordering Problem and Generalized Bell Numbers

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dc.creatorBlasiak, P.
dc.creatorPenson, K. A.
dc.creatorSolomon, A. I.
dc.date2002-12-11
dc.date.accessioned2026-07-07T06:05:42Z
dc.date.available2026-07-07T06:05:42Z
dc.descriptionFor any function F(x) having a Taylor expansion we solve the boson normal ordering problem for F[(a*)^r a^s], with r,s positive integers,[a,a*]=1, i.e. we provide exact and explicit expressions for its normal form which has all a's to the right. The solution involves integer sequences of numbers which, for r,s >=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.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0212072
dc.identifierhttp://arxiv.org/abs/quant-ph/0212072
dc.identifierAnnals of Combinatorics 7: 127-139, (2003)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/90724
dc.subjectQuantum Physics
dc.subjectCombinatorics
dc.titleThe Boson Normal Ordering Problem and Generalized Bell Numbers
dc.typetext

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