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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
Normal Ordering in the Weyl Algebra Further Aspects 193
6.1.4 The Identity of Bender, Mead, and Pinsky
In this section, we describe an identity first observed by Bender, Mead, and Pinsky
[82, 83] and discussed in the context of operator ordering by Bender and Dunne [81]. It
was first proved by Koornwinder [680], who used several intricate relations. Later, it was
reproved and discussed by other authors [527,1004]. We follow the presentation given in [527]
and consider the Weyl algebra A
i
generated by U and V satisfying UV VU = i.Letus
denote by T
n,m
the sum of all possible terms containing n factors of U and m factors of
V .Also,T
n
= T
n,n
. For example, ...
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Publisher Resources

ISBN: 9781466579897