Customer Reviews

Lectures on Quantum Theory: Mathematical

5 star:		(5)
4 star:		(0)
3 star:		(1)
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1 star:		(0)

 

 

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.

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.

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.

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.

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.

Very fine lectures on the foundations of quantum mechanics but definitely not for beginners. Prof. Isham states: "These lectures were part of a third year theoretical physics option (preface, p. v)", so be prepared. Before tackling this book on your own, I think you should understand something about vector spaces, basic linear functional analysis and Hilbert spaces and also feel comfortable with a fairly high degree of mathematical and logical abstraction.

Prof. Isham's exposition is admirably clear and he provides a great deal of very helpful discussion of a number of difficult / subtle foundational issues, concepts and theorems central to quantum mechanics. The topics go well beyond what's in introductory or even more advanced textbooks, e.g. in chapter 4, he discusses the classical physics notion of property, which is compared to the quantum mechanical situation; in chapter 5 (General Formalism of Quantum Theory), he states informally and elucidates four rules providing the basic conceptual underpinnings of QM. Rule 3 deals with the central notion of expected result of measuring an operator on a quantum state and then later in section 5.3, he discusses in detail an alternative form of rule 3 and its implications, all of which I found quite interesting. Chapter 6 discusses a number of key technical topics including density matrices, a subject typically missing from introductory accounts. Chapter 7 includes a nice discussion of uncertainty relations. Chapter 8 (Conceptual Issues in Quantum Theory) and Chapter 9 (Properties in Quantum Physics) is where he really gets into various controversial topics: the meaning of probability, reduction of state vectors, quantum entanglement, the measurement problem, all in ch. 8; followed by the Kochen-Specker theorem, quantum logic and non-locality and Bell's inequalities, all in ch. 9. It is really wonderful to be able to learn how a world-class theoretical physicist like Prof. Isham, who takes conceptual issues seriously unlike many practicing quantum physicists, thinks about these arguably arcane issues. These discussions are introductory and somewhat superficial but nevertheless insightful and well worth one's time.

In summary, if you're interested in the deep and perplexing conceptual issues of quantum mechanics then these lectures will provide you with a pedagogically sound, totally reliable introduction by a world-class physicist who is also a gifted writer.