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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
188 Commutation Relations, Normal Ordering, and Stirling Numbers
We will give a proof of the q-deformed version of this identity later in Section 7.2.4. The
same method of proof shows that one also has (VUV)
n
= V
n
U
n
V
n
. Equation (6.18) can
be generalized to the product having m factors of VU inside the parentheses, that is, one
has that
(UVU···VU
! "
m times VU
)
n
= U
n
V
n
U
n
···V
n
U
n
! "
m times V
n
U
n
. (6.19)
In the representation U → D, V → X ˆx x, identity (6.18) becomes
(DxD)
n
= D
n
x
n
D
n
, (6.20)
which is the result (6.17) of Tait.
Let us turn to an application. Carlitz [189] considered the expansion of (DxD)
n
and
found that
(DxD)
n
=
n
k=0
n
k
n!
k!
x
k
D
n+k
, (6.21) ...
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Publisher Resources

ISBN: 9781466579897