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Mathematical concepts of quantum mechanics. (English) Zbl 1033.81004

Universitext. Berlin: Springer (ISBN 3-540-44160-3/pbk). x, 249 p. (2003).
This books presents a competent and interesting pedagogic account of certain topics in functional analysis and their applications to a selection of problems in quantum mechanics, quantum field theory and quantum statistical mechanics. The typography and page layouts are, as one expects in a Springer publication, superb. However, one must add that the title is misleading. Quantum mechanics uses practically every branch of mathematics and has significantly influenced the development of each branch used. Such branches which deserve special mention include group theory, ring theory, lattice theory, topology, topological dynamics, manifold theory, tensor analysis and probability theory and they are all more or less ignored in this book as are certain concepts in functional analysis such as rigged Hilbert space, distribution theory and the Dirac formalism. These lists are by no means exhaustive.

MSC:

81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
81Sxx General quantum mechanics and problems of quantization
82-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
46N50 Applications of functional analysis in quantum physics
81Txx Quantum field theory; related classical field theories
47N50 Applications of operator theory in the physical sciences
82B10 Quantum equilibrium statistical mechanics (general)
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