Gustafson, Stephen J.; Sigal, Israel Michael 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. Reviewer: Chandra Shekhar Sharma (London) Cited in 3 ReviewsCited in 20 Documents 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) Keywords:functional analysis; quantum mechanics; spectral theory; quantum field theory; quantum statistical mechanics PDFBibTeX XMLCite \textit{S. J. Gustafson} and \textit{I. M. Sigal}, Mathematical concepts of quantum mechanics. Berlin: Springer (2003; Zbl 1033.81004) Full Text: DOI