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© 2008

Hilbert Space Operators in Quantum Physics

Benefits

  • Self-contained and in-depth exposition of the foundations of quantum theory

  • The second edtion of this successful book contains chapters on new and important subjects such as quantum waveguides and quantum graphs

  • Includes up to 500 problems ranging from simple exercises to deeper questions testing the reader’s full understanding

  • Extensive bibliography containing monographs as well as numerous research papers

Book

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Pages 41-62
  3. Pages 63-92
  4. Pages 93-150
  5. Pages 151-204
  6. Pages 251-292
  7. Pages 293-316
  8. Pages 317-356
  9. Pages 379-402
  10. Pages 403-424
  11. Pages 443-490
  12. Pages 491-526
  13. Pages 527-560
  14. Pages 561-593
  15. Back Matter
    Pages 617-664

About this book

Introduction

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

Keywords

Hilbert space Hilbert-space operators Quantum graphs Quantum physics Quantum waveguides Second quantization Self-adjoint operators Spectral theory functional analysis

Authors and affiliations

  1. 1.Charles UniversityPragueCzechia
  2. 2.Doppler Institute and Nuclear Physics InstituteCzech Academy of SciencesPragueCzech Republic
  3. 3.Doppler Institute and Faculty of Nuclear Sciences and Physical EngineeringCzech Technical UniversityPragueCzech Republic

About the authors

Jirí Blank graduated in 1961 from Czech Technical University and got his PhD from Charles University. Until his premature death in 1990 he was active in mathematical-physics research and teaching. He educated many excellent students.

Pavel Exner graduated in 1969 from Charles University. From 1978 to 1990 he worked in Joint Institute for Nuclear Research, Dubna, where he got his PhD and DSc degrees. After the return to Prague he headed a mathematical-physics group in the Nuclear Physics Institute of Academy of Sciences and became a professor of theoretical physics at Charles University. He authored over 150research papers to which more than thousand citations can be found. At present he is a vice president of European Mathematical Society and secretary of IUPAP commission for mathematical physics.

Miloslav Havlícek graduated in 1961 from Czech Technical University; he got his PhD from Charles University and DSc at Joint Institute for Nuclear Research, Dubna. He wrote numerous papers on algebraic methods in quantum physics. From 1990 he served repeatedly as dean of the Faculty of Nuclear Sciences and Physical Engineering and head of the Department of Mathematics.

Bibliographic information

Reviews

From the reviews of the second edition:

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)

"This is an excellent textbook for graduate students and young researchers in mathematics and theoretical physics. … 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." (Michael Demuth, Zentralblatt MATH, Vol. 1163, 2009)

“As the title declares, the text presents a comprehensive presentation of linear spaces and their transformations. … this second edition contains two additional chapters on quantum treatments of waveguides and graphs. … The book considered is, no doubt, written for physicists and useful for them. … A valuable feature of this book is the extensive background material and discussions collected into separate sections. … The book does what it promises and does it well.” (Stig Stenholm, Contemporary Physics, January, 2010)