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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
Appendix F
Hilbert Spaces and Linear Operators
John von Neumann gave the first precise formulation of quantum mechanics in 1928/1929
and a systematic account in his famous book [1119] from 1932 using the formalism of
unbounded self-adjoint operators in Hilbert space. A modern presentation can be found in
[926,1059,1131]. In this appendix we briefly recall some of the basic mathematics, following
closely [926, 1059, 1131].
F.1 Basic Facts on Hilbert Spaces
To start with, let us recall that an inner product space is a complex vector space V in
which a complex valued function (·, ·):V × V C is defined which satisfies
(i)(x, x) 0and(x, x) = 0 if and
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Publisher Resources

ISBN: 9781466579897