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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
416 Commutation Relations, Normal Ordering, and Stirling Numbers
U(t + s)=U(t)U (s) is very natural to assume as well as the property of being strongly
continuous (by a theorem of John von Neumann it is enough to assume the measurability of
the matrix elements), so that Stone’s theorem implies that U (t)=e
itH
for some self-adjoint
operator H. For all f D(H) one has with ψ(t)=U(t)f that
1
i
d
dt
ψ(t)=(t)whichis
an abstract version of Schr¨odinger’s equation.Thus,theHamiltonian operator H has to be
self-adjoint.
F.3 Basic Facts on Spectral Theory
Let us turn to some points concerning spectral theory. Recall that in C
n
a symmetric
linear map T can be diagonalized ...
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Publisher Resources

ISBN: 9781466579897