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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
198 Commutation Relations, Normal Ordering, and Stirling Numbers
Now, we would like to recall some normal ordering results discussed already in Sec-
tion 5.3. The result (6.45) is due to McCoy [789] and Schwinger [985] (but see also the
closely related work of Sylvester [1051]), while (6.47) seems to be due to Mehta [795, 796]
and Wilcox [1142].
Theorem 6.30 Let U and V be generators of the extended Weyl algebra
ˆ
A
1
satisfying
[U, V ]=1. Then one has for any λ C
e
λV U
=:e
(e
λ
1)VU
: . (6.45)
If N = VU, then we can write (6.45) equivalently as
e
λN
=:B(λ, N):, (6.46)
where B(x, y)=e
(e
x
1)y
denotes the exponential generating function of the Bell polynomi-
als. ...
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Publisher Resources

ISBN: 9781466579897