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Commutation Relations, Normal Ordering, and Stirling Numbers
book

Commutation Relations, Normal Ordering, and Stirling Numbers

by Toufik Mansour, Matthias Schork
September 2015
Intermediate to advanced content levelIntermediate to advanced
528 pages
19h 34m
English
Chapman and Hall/CRC
Content preview from Commutation Relations, Normal Ordering, and Stirling Numbers
Introduction 11
discussed the symbolical content of Hargreaves’s results and introduced for that purpose
symbols π and ρ satisfying
πρ ρπ = α, (1.14)
where α was assumed to commute with π and ρ. Graves discussed that a particular represen-
tation for this commutation relation is given (for α =1)byπ → D =
d
dx
and ρ → X,where
X denotes again the operator of multiplication with the independent variable x. He also
showed that this commutation relation implies an abstract version of Hargreaves’ results.
In fact, a few years earlier, in 1850, Donkin [362] had considered a more general situation
in which symbols ω, ρ
1
,...,ρ
n+1
are involved which satisfy
ωρ
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Publisher Resources

ISBN: 9781466579897