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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
218 Commutation Relations, Normal Ordering, and Stirling Numbers
6.6.1 The Bosonic Case
In the general case where r modes are present, the creation resp. annihilation operators
ˆa
k
resp. ˆa
k
(with k =1,...,r) satisfy the commutation relations (5.33). To simplify the
notation, we consider only two modes and denote the operators by {ˆa, ˆa
,
ˆ
b,
ˆ
b
}.Allof
the operators {ˆa, ˆa
} commute with all of the operators {
ˆ
b,
ˆ
b
}, and each of these two
sets represents the creation resp. annihilation operator of a harmonic oscillator. From a
physical point of view, the two modes do not interact (that is, they are not coupled). Let
us also introduce the number operators ...
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Publisher Resources

ISBN: 9781466579897