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Lectures on Quantum Theory: Mathematical and Structural Foundations [Paperback]

C.J. Isham
4.7 out of 5 stars  See all reviews (3 customer reviews)
Price: 20.00 & FREE Delivery in the UK. Details
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Book Description

9 Jan 1995 1860940013 978-1860940019
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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Product details

  • Paperback: 232 pages
  • Publisher: Imperial College Press (9 Jan 1995)
  • Language: English
  • ISBN-10: 1860940013
  • ISBN-13: 978-1860940019
  • Product Dimensions: 1.5 x 15.5 x 20.4 cm
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Bestsellers Rank: 497,612 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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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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Customer Reviews

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Most Helpful Customer Reviews
6 of 6 people found the following review helpful
5.0 out of 5 stars Beautifully written and quite indispensible 23 Oct 2000
By A Customer
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.
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3 of 4 people found the following review helpful
By A Customer
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.
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5.0 out of 5 stars a classic 22 Jun 2012
Format:Paperback|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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Most Helpful Customer Reviews on (beta) 4.7 out of 5 stars  7 reviews
16 of 16 people found the following review helpful
5.0 out of 5 stars Illuminating 9 July 2002
By Aquinatis - Published on
In this book Prof. Isham exposes the minimum algebra required for quantum physics, from vector spaces to eigenvalues, Hilbert spaces, density matrices, and equations specific to quantum theory (e. g. entanglement, EPR, Bell, etc.) He does not give unnecessary details but many insights that make the concepts used in algebra more tangible, more understandable, explaining the idea being the various mathematical theories he deals with. of . I read this book for the quantum aspect, but it may have profited me more for the math, for the deeper understanding it gave me of those mathematical concepts. In addition, Isham offers many sound philosophical (yet short, clear and to the point) discussions on the concepts involved, on probabilities, truth, measurement problem, many worlds, non-locality, etc. The book is a masterful treatment combining algebra, physics and philosophy. Add to this some exercises with answers, and here is a book that you don't want to miss, if you already have some basic knowledge of mathematics and quantum physics.
11 of 11 people found the following review helpful
5.0 out of 5 stars Deep and balanced 22 May 2001
By Georg - Published on
If you are an undergraduate physicist or have an equivalent mathematical background this is the best book to understand the mathematical structure and the conceprual basis of quantum theory. The presentation is at a level accessible to undergraduates, however there are many side remarks and comments that slowly introduce you to understanding different foundational issues (that often cannot be accessed without a larger mathematical background). It is the deepest modern introductory textbook in quantum mechanics that I have read.
10 of 10 people found the following review helpful
5.0 out of 5 stars Very Good 13 April 2003
By A Customer - Published on
This book is for all those who want to understand more about quantum mechanics. It explains in a very intelligent way the essential differences between a classical theory and a quantum mechanical one. Highly recommended. You will not learn from this book on how to solve e.g. scattering problems, this book focuses on understanding the theory rather than applying it. I enjoyed it very much.
8 of 8 people found the following review helpful
5.0 out of 5 stars Essential for the well-rounded physicist 27 April 1999
By A Customer - Published on
This is the way a subject as complex as Quantum Theory should be taught ! Prof Isham not only offers a very clear presentation of all the essential mathematics, but also very interesting comments and insights concerning philosophical aspects of Quantum Theory. Excellent presentation of a very tough subject - I really appreciated it even though my area is stellar astrophysics. Not one page is boring and the whole is very well structured. Note that a preliminary overview of basic quantum mechanics certainly helps.
9 of 10 people found the following review helpful
3.0 out of 5 stars Not that easy, but ... 4 Sep 2002
By A Customer - Published on
I appreciate the author's approach as much as the other, "five star" reviews. Isham has tackled some very difficult material and consistently gone to the heart of the problems involved with the meaning of quantum theory. He has treated the many different approaches - from pure pragmatism to hidden variables and many worlds - with fairness and due respect for each. My only disagreement with the other reviewers is their assessment of the book's accessibility. The mathematics is heavy on abstractions. As a former graduate student in physics (admittedly long ago), I found it rougher going than I expected and spaced out several of the final subjects such as quantum logic. Nevertheless I came away with a better understanding of the foundations of quantum mechanics, and I have no regrets over buying the book.
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