Combinatorics of Boson Normal Ordering: the Dobinski Formula Revisited

Details Combinatorics of Boson Normal Ordering: the Dobinski Formula Revisited Combinatorics of Boson Normal Ordering: the Dobinski Formula Revisited

2002-11-06

arxiv.org/abs/quant-ph/0211028v1

Physics

Quantum Physics

4 pages. Proceedings of Group 24, Paris, July 2002

Scientific paper

We derive explicit formulas for the normal ordering of powers of arbitrary monomials of boson operators. These formulas lead to generalisations of conventional Bell and Stirling numbers and to appropriate generalisations of the Dobinski relations. These new combinatorial numbers are shown to be coherent state matrix elements of powers of the monomials in question. It is further demonstrated that such Bell-type numbers, when considered as power moments, give rise to positive measures on the positive half-axis, which in many cases can be written in terms of known functions.

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