dorsal/arxiv
View SchemaThe Boson Normal Ordering Problem and Generalized Bell Numbers
| Authors | P. Blasiak, K. A. Penson, A. I. Solomon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212072 |
| URL | https://arxiv.org/abs/quant-ph/0212072 |
| Journal | Annals of Combinatorics 7: 127-139, (2003) |
Abstract
For 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.
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"abstract": "For any function F(x) having a Taylor expansion we solve the boson normal\nordering problem for F[(a*)^r a^s], with r,s positive integers,[a,a*]=1, i.e.\nwe provide exact and explicit expressions for its normal form which has all a\u0027s\nto the right. The solution involves integer sequences of numbers which, for r,s\n\u003e=1, are generalizations of the conventional Bell and Stirling numbers whose\nvalues they assume for r=s=1. A complete theory of such generalized\ncombinatorial numbers is given including closed-form expressions (extended\nDobinski - type formulas), recursion relations and generating functions. These\nlast are special expectation values in boson coherent states.",
"arxiv_id": "quant-ph/0212072",
"authors": [
"P. Blasiak",
"K. A. Penson",
"A. I. Solomon"
],
"categories": [
"quant-ph",
"math.CO"
],
"journal_ref": "Annals of Combinatorics 7: 127-139, (2003)",
"title": "The Boson Normal Ordering Problem and Generalized Bell Numbers",
"url": "https://arxiv.org/abs/quant-ph/0212072"
},
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