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Hilbert space operators in quantum physics. 2nd ed. (English) Zbl 1163.47060
Theoretical and Mathematical Physics (Cham). New York, NY: AIP Press; Berlin: Springer (ISBN 978-1-4020-8869-8/hbk; 978-1-4020-8870-4/ebook). xviii, 664 p. (2008).
This is an excellent textbook for graduate students and young researchers in mathematics and theoretical physics. The book is divided into two parts.
The first, mathematical part describes the theory of linear operators in Hilbert spaces. It is a course from the basics in functional analysis to bounded and unbounded operators, including spectral theory and operator algebras. The exposition is comprehensive, but self-contained.
The second part is devoted to the mathematical theory of quantum mechanics. It treats the following topics: axiomatics, states, observables, position and momentum; time evolution and Feynman integrals, symmetries, second quantization; Schrödinger operators, scattering theory, quantum waveguides, quantum graphs.
[The first edition appeared 1994 and was reviewed in Zbl 0873.46038.]

47N50 Applications of operator theory in the physical sciences
46N50 Applications of functional analysis in quantum physics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
46L60 Applications of selfadjoint operator algebras to physics
46L30 States of selfadjoint operator algebras
47-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory
46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
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