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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 213
the operators act (to the right). For example, one has
1
A
2
B = BA, (
1
A +
2
B)
2
=(
1
A)
2
+2
1
A
2
B +(
2
B)
2
= A
2
+2BA + B
2
.
Note that only the relative size of the indices is important, and instead of the pair (1, 2) one
could also use (4, 13); there exist several rules for dealing with these indices [779, 862,863].
For a polynomial (or also formal series) one indicates in the same fashion the order of the
operator arguments. For example, if p(x, ξ)=
n
k=0
a
k
(x)ξ
k
denotes a polynomial in x and
ξ,then
P
2
x,
1
d
dx
=
n
k=0
a
k
(x)
d
k
dx
k
denotes the associated differential operator in standard form (and p(x, ξ) denotes
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Publisher Resources

ISBN: 9781466579897