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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
16 Commutation Relations, Normal Ordering, and Stirling Numbers
with Heisenberg , they derived for any function f (q, p), which can be formally expressed as
power series in p and q,therule
pf f p =(i)
∂f
q
,
as well as
qf f q =(i)
∂f
p
. (1.33)
Dirac, who independently found (1.31) in [349], considered in his subsequent work [351]
algebraic consequences of (1.31) and also derived (1.33). Furthermore, Dirac showed that
f(q, p)e
q
= e
q
f(q, p + α),
which one recognizes as (1.12) already discussed by Boole or, even earlier, by Cauchy
(1.11). Dirac [350] considered many other interesting consequences of (1.31). Coutinho [304]
gave a beautiful account ...
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Publisher Resources

ISBN: 9781466579897