Based on material taught to final-year students of theoretical physics, this is an introduction to the essentials of vector spaces and linear operators. It builds bridges between the concepts and mathematics of classical physics, and the mathematical framework employed in quantum mechanics. The axioms of nonrelativistic quantum theory are introduced, and shown to lead to a variety of new conceptual problems. Subjects discussed include state-vector reduction, the problem of measurement, quantum entanglement, the Kochen-Specker theorem, and the Bell inequalities. The book includes 25 problems with worked solutions.
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"In the US it could serve as an excellent supplement for an introductory graduate course on quantum mechanics ... The discursive style and clear exposition make for equally attractive reading by someone familiar with the subject or by a student with only rudimentary knowledge ... The main text is supplemented by a substantial number of problems with solutions, which should help the beginner master the mathematics ... I would strongly recommend that anyone teaching the subject use this little book as supplementary reading." Physics Today (USA), Aug 1996 "The proper role of mathematics is to make things easy. When something can be expressed in the precise language of mathematics, results can be obtained by the application of given rules. Calculations are so simple that even computers can do them. Chris Isham's lectures on the mathematical and structural foundations of quantum theory, reproduced in this book, provide an excellent illustration of this truth ... a welcome addition to the modern literature on quantum theory. It is good to have a book that gives such an excellent description of the mathematical structure of quantum theory, written by an author who recognises the need to understand its meaning." Times Higher Educational Supp. (UK), Mar 1996 "Chris Isham's book is a welcome addition to the existing literature. If you already have some familiarity with quantum theory and you want one book -- get this one!" Science 2000 "... this is a clear, elegant and beautifully structured introductory account of some of the most puzzling aspects of physics ... I believe that this book will be particularly influential, however, because it makes the basic philosophical ideas and the mathematical theorems that underpin the rapidly developing field of quantum technology so accessible ... The novice can seek no more cultured or congenial guide than Chris Isham. I am convinced that this book -- to indulge in that hackneyed but totally appropriate phrase -- is destined to become a classic." Physics World, 1996 "The book is well structured and written with remarkable clarity ... can be recommended both as a very good textbook for students as well as for lecturers who are interested in the fundamental conceptual problems of quantum theory..." Reports on Mathematical Physics, Jun 1997
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6 of 6 people found the following review helpful
By A Customer
Format:Hardcover
Elementary wave mechanics is built into the more abstract formalism of quantum theory proper. Although the treatment is fairly rigorous, the writing is so clear and elegant that the mathematics never obscures the physical motivation. Interesting comparisons are drawn between the logical structures of classical and quantum physics. I would challenge any physicist not to learn something from this book. A first-class introduction to quantum theory.
3 of 4 people found the following review helpful
By A Customer
Format:Hardcover
This is NOT a standard introduction to quantum mechanics, i.e. you will not learn how to use it in practical situations.
It is about the mathematical structure, and how it differs from the classical one. In respect to this there are really some very original and authentic ideas in it, that you will not find in any other book, e.g. the kochen-specker theorem is put in a very clear perspective.
Personally I found it a pity that he waisted half of his book on the easy mathematics of vector spaces, but if you are new to the subject, it seems well explained. Also he avoided touching the harder mathematics. Gleason's theorem (the most important theorem for the qm structure) is only touched. I also skipped the philosopical pages when reading.
But anybody who is interested in the math. struct. of physics SHOULD buy this book because of the rich ideas you will find in it.
Format:Paperback|Amazon Verified Purchase
I have had this book for many years but mislaid my copy so bought it again. Isham writes with clarity and authority (his other books in this series are excellent, too) so what more is there to say - oh yes, the book is very useful and a very handy reference at this level - hence my need to replace my "lost" copy
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