Hilbert Space Operators in Quantum Physics
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This course-tested book explains in detail the theory of linear Hilbert-space operators and their use in quantum physics. The central mathematical tool of the book is the spectral theory of self-adjoint operators; in order to make the exposition self-contained, selected topics of functional analysis are included. An introduction to the theory of operator sets and algebras is also presented. This mathematical material is then used for a systematic analysis of the operator structure of quantum theory. Logical building of the theory is discussed as well as its practical aspects, such as spectral properties of quantum mechanical Hamiltonians, scattering theory, and more.
The second edition was extended by two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography was amended by about 130 new items.
The second edition was extended by two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography was amended by about 130 new items.
The second edition of this course-tested book provides a detailed and in-depth discussion of the foundations of quantum theory as well as its applications to various systems. The exposition is self-contained; in the first part the reader finds the mathematical background in chapters about functional analysis, operators on Hilbert spaces and their spectral theory, as well as operator sets and algebras. This material is used in the second part to a systematic explanation of the foundations, in particular, states and observables, properties of canonical variables, time evolution, symmetries and various axiomatic approaches. In the third part, specific physical systems and situations are discussed. Two chapters analyze Schrödinger operators and scattering, two others added in the second edition are devoted to new important topics, quantum waveguides and quantum graphs.
Some praise for the previous edition:
"I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone...." John R. Taylor, Professor of Physics and Presidential Teaching Scholar, University of Colorado at Boulder
Some praise for the previous edition:
"I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone...." John R. Taylor, Professor of Physics and Presidential Teaching Scholar, University of Colorado at Boulder
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