Intermediate Spectral Theory and Quantum Dynamics (Progress in Mathematical Physics, 54)

De Oliveira, César R.

ISBN 10: 3764387947 / ISBN 13: 9783764387945

Published by Birkhäuser, 2008

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Bibliographic Details

• Title: Intermediate Spectral Theory and Quantum Dynamics (Progress in Mathematical Physics, 54)
• Publisher: Birkhäuser
• Publication Date: 2008
• Language: English
• ISBN 10: 3764387947
• ISBN 13: 9783764387945
• Binding: Hardcover
• Condition: New

About this title

Synopsis

The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. Furthermore, such a rigorous mathematical foundation leads to a more profound insight into the nature of quantum mechanics. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics.

The book places emphasis on the symbiotic relationship of these two domains by (1) presenting the basic mathematics of nonrelativistic quantum mechanics of one particle, i.e., developing the spectral theory of self-adjoint operators in infinite-dimensional Hilbert spaces from the beginning, and (2) giving an overview of many of the basic functional aspects of quantum theory, from its physical principles to the mathematical models.

The book is intended for graduate (or advanced undergraduate) students and researchers interested in mathematical physics. It starts with linear operator theory, spectral questions and self-adjointness, and ends with the effect of spectral type on the large time behaviour of quantum systems. Many examples and exercises are included that focus on quantum mechanics.

Review

From the reviews:

"The aim of Intermediate Spectral Theory and Quantum Dynamics is to provide advanced undergraduate and graduate students with this understanding of the mathematical intricacies of non-relativistic quantum mechanics of a single particle. ... a concise introduction to the spectral theory of unbounded operators ... . ends with a comprehensive bibliography which contains references to the original literature and further reading and an extensive index of the material presented. ... I have found this book an interesting read which I will consult in future ... ." (Jörg Bernhard Götte, Contemporary Physics, Vol. 52 (3), May-June, 2011)

"The book gives an introduction to spectral theory on the graduate or advanced undergraduate level. ... The variety of topics is remarkably large for a book at the textbook level, and also some recent results are included. ... In conclusion, Intermediate spectral theory and quantum dynamics is a mostly complete and very readable introduction to this classical area of mathematics. Students will surely appreciate the many examples and exercises." (Rupert L. Frank, Mathematical Reviews, Issue 2011 m)