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arxiv: quant-ph/0510082 · v1 · submitted 2005-10-12 · 🪐 quant-ph

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Combinatorial Solutions to Normal Ordering of Bosons

P. Blasiak (1 , 2) , A. Gawron (1) , A. Horzela (1) , K.A. Penson (2) , A.I. Solomon (2 , 3) ((1) Institute of Nuclear Physics , Polish Academy of Sciences
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Krakow Poland (2) LPTMC University of Paris VI France (3) The Open University Milton Keynes UK)
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classification 🪐 quant-ph
keywords combinatorialbellnormalorderingsolutionsallowbosonbosons
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We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions - the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead to calculational tools which allow to find explicitly normally ordered forms for a large class of operator functions.

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