Hilbert Space Operators in Quantum Physics (Theoretical and Mathematical Physics) by Jirí Blank (PDF)

Description

The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

User’s Reviews

Editorial Reviews: Review 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) From the Back Cover 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 About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Very nice, clear, self contained textbook covering huge amount of topics from functional analysis and quantum physics. Mathematically rigorous textbook, mathematicians will love it.

⭐This is one of my favorite go-to references on the mathematically rigorous details of quantum theory. When I need to cite a definition/theoem/etc, I normally find it here. It’s certainly not a first textbook on quantum theory, in presuming that you have the basic idea but perhaps could use a better grip on some of the mathematics. Extremely handy thing to have within arm’s reach on the desk of the mathematical physicist. Unfortunately, there is not a Kindle version yet, but once you’ve purchased the book you can find a text-recognized PDF on bookfi/freesci, which is useful when you want to search for a specific passage or term.

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