Book Description
Designed for students familiar with abstract mathematics but not physics, this graduate-level text was written by a member of the National Academy of Science. It introduces fundamentals of classical mechanics; surveys basics of quantum mechanics; and concludes with a look at group theory and quantum mechanics of the atom. 1963 edition.
Customer Reviews:
Mathematical Physics.......2007-10-08
This book tries to cover, (but not with success) the needed mathematics for learning or teaching Quantum Mechanics. The contains of a course in Mathematical Foundations of Quantum Mechanics must include mainly two branches of Mathematics: Group theory and Operator theory. The corresponded chapters in the book are short. This book, written in a high level, is difficult to be understood by undergraduate students. It is proper for postgraduates
Power Math for Physics.......2006-11-12
In 2004 Dover re-released this classic of higher mathematics originally published in 1963.
The author discovered that one of the big difficulties of teaching Quantum Mechanics is that most of the time is spent fighting with the mathematics involved. He wrote this book to address that need.
This text is aimed at advanced undergraduates or graduate students in the areas of advanced mathematics, physics and quantum mechanics. It assumes a previous knowledge of Calculus, Advanced Calculus, Differential Equations and some college level physics.
The text is divided into three parts covering Classical Mechanics, Quantum Mechanics, Group Theory and the Quantum Mechanics of the atom.
If you are afraid of math, be afraid. Be very afraid.
If your mathematical curiosity is greater than your fear OR you are a student of physics, this book fills, in one volume, a much needed niche.
Why not Dover?.......2003-02-24
I wish this out-of-print book would be in the collection of Dover. Now it's hard to find it, but still many physics & math people are looking for it and discussing about it.
Geroge Mackey, Hermann Weyl, and John von Neumann are the mathematical foundations of Q.M.
Average customer rating:
- Nice condensed book
- a good source for a "quick review"
- better than most professors, but...
- Not really a very good book
- Very helpful, but also very theoretical
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Schaum's Outline of Continuum Mechanics
George Mase
Manufacturer: McGraw-Hill
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Continuum Mechanics: Concise Theory and Problems
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Schaum's Outline of Tensor Calculus (Schaum's)
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Schaum's Outline of Finite Element Analysis
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Continuum Mechanics for Engineers, Second Edition
ASIN: 0070406634 |
Book Description
For comprehensive—and comprehensible—coverage of both theory and real-world applications, you can’t find a better study guide than Schaum’s Outline of Continuum Mechanics. It gives you everything you need to get ready for tests and earn better grades! You get plenty of worked problems—solved for you step by step—along with hundreds of practice problems. From the mathematical foundations to fluid mechanics and viscoelasticity, this guide covers all the fundamentals—plus it shows you how theory is applied. This is the study guide to choose if you want to ace continuum mechanics!
Customer Reviews:
Nice condensed book.......2007-09-07
This is a great book to support all the information you can get in a single continuum mechanics class. It could be nice if it has a more detailed treatment of the mohr's circle because of his power in 2D and an approach to the analysis of shells and plates.
Best regards and enjoy it!
a good source for a "quick review".......2003-12-03
Like most other Schaum's series, the theory sections are condensed, which makes the part more like a compendium of continuum mechanics. The theoretical sections are thus good for a quick review of the material but not a good resource for "learning" the material. The biggest advantage of the book is that it provides an inexpensive summary of continuum mechanics.
The downside of the book is that the solved problems are not similar to the type of problems one confronts in a typical continuum course. In most cases several problems (statement together with the solution) are presented in a single page, which shows that each problem has been solved in 1-5 lines. I personally don't like most of the problems presented here; however, the problems could be useful for warming up.
A better book is "Introduction to the Mechanics of a Continuous Medium" by Malvern, which is the best I've seen in explaining the intricacies of the theory. Another good complement is Holzapfel's "Nonlinear Solid Mechanics: A Continuum Approach for Engineering", which contains both the theory AND some solved sample problems.
better than most professors, but..........2003-04-13
Better than most professors, but concepts are still difficult to grasp. Have you ever had one of those tennis ball machines go crazy at you? That is how continuum mechanics is, you constantly have things hurled in your direction and you don't know how to stop them. The concepts are very difficult to understand since I'm sure many professors have a hard time understanding the course material itself. The Schaum's outline helps very much in the sense that it slows down the hurling of material and it explains where many equations are derived from. This book stands out above the rest of continuum mechanics books in the sense that it offers solved problems, which is rare for such a theoretical class.
Not really a very good book.......2003-03-26
Not really a very good book on continuum mechanics. However, it
does summarise some very important points and equations useful
for quick reference. The exercise is not so great.
Very helpful, but also very theoretical.......2000-03-28
The problems in this book where very helpful to me in my applied continuum mechanics course, but they tended more towards the theoretical side. A good purchase for students and researchers dealing with solid mechanics and mechanics of materials.
Book Description
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.
Customer Reviews:
.. and try to read everything else JvN wrote, too!.......2005-11-19
von Neumann's account of why he uses the mathematics he does and his critique of the Dirac formalism is worth the price of admission. Those who deride him for avoiding the delta formalism seem to have been seduced by its meretricious computational facility. von Neumann anticipated - actually began in this book and his work on continuous geometry - the modern approach via non-commutative geometry to physics (see Alain Connes), and M-theory.
Hilbert Space Formulation of QM.......2003-04-10
The ultimate source of Hilbert Space applied to Quantum Mechanics. John von Neumann was the first to systematically formulate QM in such a powerful and elegant vector space. If this is the Bible of QM in HS, Hughes is the missioner! Get the book as well -- The Structure and Interpretation of Quantum Mechanics.
Has Strengths and Weaknesses.......2002-07-30
First the strengths:
(1) The author gives a rigorous proof of the incompatibility of the two theories of quantum mechanics, that is, the evolution of the state vector as determined by Schrodinger's equation and the collapse of the state vector by means of an observation. He does this by the concept of entropy.
(2) He gives a thorough treatment of the "consciousness school" of interpretation, which makes for an interesting,if not entirely convincing read.
The weaknesses:
(1) the font is a pain to read; it looks like it came off an old typewriter. I wonder why the publishers couldn't put it into a more modern readable form.
(2) Von Neumann writes this book , in part, with the intention to dispel the mathematical nonsense, as he perceives it, of the Dirac delta function. Therefore he casts everything into the unwieldy formalism required to do without the distribution. Indoubtedly he was trying to change the dirac formalism in use in quantum mechanics at the time but was fortunately unsucessful in persuading physicists to use his alternative language.
Summary: I recommend this book for anyone wishing to deepen his or her understanding of the foundations, conceptual and mathematical of quantum theory.
a classic.......2000-08-23
As an undergrad, I am sorry that I cannot share the perspectives of professionals as expressed below. After initial introductory courses, I got fascinated by certain untold conceptual issues. And one of the textbooks (probably Griffiths) suggested von Neumann had tried to prove mathematically that the classical formulation is just the furthest the formalism can go and we don't have to worry about underlying complexities. Later, Bohm created a formalism which von Neumann "proves" to be mathematically impossible in this book. I bought this book just to find out how the proof goes. But I got stuck with some tedious proofs on Hilbert space (which he calls a "digression"). This part isn't essential but as the braket notation is not used you need to consult this part. I think at least a strong background in linear algebra is required. Definitly not an introductory textbook. Most useful for those who study history of physics.
Very nice historical approach.......2000-02-01
This is not the kind of book I would recommend to a novice person in the area, but it does give a very interesting view of how was quantum mechanics born. It begins with a thorough discussion about the mathematics of Hilbert spaces and operator theory to later merge Heisenberg's and Schrodinger's theories in one rigorous mathematical theory. It makes some remarks that allows the reader to see how was the 'new' quantum theory born and developed, since it briefly discusses the theories of Heisenberg and Schrodinger in the way they originally stated them. Maybe the most disturbing issue would be the notation since in 1932 dirac had still not developed the bracket formalism.
Book Description
Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations. It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase. It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics). The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space. As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed. Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them.
Book Description
Providing a textbook introduction to the formalism, foundations and applications of quantum mechanics, Part I covers the basic material necessary to understand the transition from classical to wave mechanics. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to advances in quantum physics. Intended for use in beginning graduate and advanced undergraduate courses, the volume is self-contained and includes problems to enhance reading comprehension.
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Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups (Lecture Notes in Physics , No 39)
Ludwig Pittner
Manufacturer: Springer
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ASIN: 3540605878 |
Book Description
Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics and considered to be useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.
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Quantum Theory: Reconsideration of Foundations - 3 (AIP Conference Proceedings / Mathematical and Statistical Phsyics)
Manufacturer: American Institute of Physics
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ASIN: 0735403015 |
Book Description
This Växjö conference was devoted to the reconsideration of quantum foundations. Due to increasing research in quantum information theory, especially on quantum computing and cryptography, many questions regarding the foundations of quantum mechanics, which have long been considered to be exclusively of philosophical interest, nowadays play an important role in theoretical and experimental quantum physics.
Book Description
This book is based on material taught to final-year physics undergraduates as part of the theoretical physics option at Imperial College. After a self-contained introduction to the essential ideas of vector spaces and linear operators, a bridge is built between the concepts and mathematics of classical physics, and the new 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 twenty-five problems with worked solutions.
Customer Reviews:
Very Good.......2003-04-14
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.
Not that easy, but ..........2002-09-04
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.
Illuminating.......2002-07-10
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.
Deep and balanced.......2001-05-22
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.
Essential for the well-rounded physicist.......1999-04-28
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.
Average customer rating:
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Foundations of Quantum Mechanics, an Empiricist Approach (Fundamental Theories of Physics)
W.M. De Muynck
Manufacturer: Springer
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ASIN: 1402009321 |
Book Description
Old and new problems of the foundations of quantum mechanics are viewed from the new perspective provided by a generalization of the mathematical formalism encompassing positive operator-valued measures. One objective is to demonstrate the crucial role the generalized formalism plays in fundamental issues as well as in practical applications, and to contribute to the development of the operational approach. A second objective is the development of an empiricist interpretation of this approach, duly taking into account the role played by the measuring instrument in quantum mechanical measurements. Copenhagen and anti-Copenhagen interpretations are critically assessed, and found to be wanting due to insufficiently taking into account the measurement interaction. The Einstein-Podolsky-Rosen problem and the problem of the Bell inequalities are discussed, starting from this new perspective. An explanation of violation of the Bell inequalities is developed, providing an alternative to the usual explanation on the basis of non-locality. This treatise is based on lecture notes of an advanced course on the foundations of quantum mechanics.
Book Description
In The Quantum Theory of Fields, Nobel Laureate Steven Weinberg combines his exceptional physical insight with his gift for clear exposition to provide a self-contained, comprehensive, and up-to-date introduction to quantum field theory. This is a two-volume work. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before, and emphasizing the reasons why such a theory should describe nature. After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and the properties of particles that follow from these principles. Quantum field theory emerges from this as a natural consequence. The author presents the classic calculations of quantum electrodynamics in a thoroughly modern way, showing the use of path integrals and dimensional regularization. His account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum electrodynamics to elementary particle physics, and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. This work will be an invaluable reference for all physicists and mathematicians who use quantum field theory, and it is also appropriate as a textbook for graduate students in this area.
Customer Reviews:
Very thorough and logical, but somewhat difficult and painful to get through.......2007-07-23
To put the review in perspective, My Background: I am a senior undergraduate engineering/physics student with an interest in mathematics and theoretical physics. This is my third QFT book.
Things I liked about the book:
- The book follows a very logical progression. I love how Weinberg presents a coherent argument based on simple physical principles (specifically Lorentz invariance and the cluster decomposition principle).
- Weinberg takes painstaking effort to avoid hand-waving, and is very careful to enumerate (and make plausible) his assumptions. In so doing, he avoids the sort of black-magic feeling I got when reading some less well written QFT books (see for example: Peskin and Schroeder, which makes a mockery of logical progression in an effort to teach you how to calculate as soon as possible).
- The book was very thorough, and often provided an original approach to the material. The coverage of renormalization seemed natural and coherent, and since the book is presented in a logical order (rather than a historical one) Weinberg avoids justifying renormalization as some mysterious subtraction of infinities, basing it instead on general non-perterbative methods (e.g. poles of the S-matrix, etc...)
What I didn't like about the book:
- As a result of his unwavering emphasis on logical progression, and his inclusion of a vast amount of material (almost all of which is necessary to understand in order to progress through the book), the book is somewhat painful to get through. Be prepared to re-read many of the sections a couple of times, and to make very slow progress.
- Weinberg chooses to present QFT in a very general form (i.e. abstracting it from a particular field such as particle physics or condensed matter physics). This is not necessarily a disadvantage, but I often found my interest waning after reading a few hundred pages without making any contact with phenomenology. Additionally, the excercises were similarly abstract, which makes it difficult (at least for me) to particularly care about their results. (More of a problem for self-study)
- The notation is very complete, which isn't normally a bad thing. However, the equations sometimes become very cumbersome when he includes every index, and every functional dependence regardless of how redundant they may be.
- In his coverage of path integrals, he derives things using functional determinants rather than through the more common generating functional methods. I think this hides a lot of the physical insight of the path integral approach, particularly, its equivalence to the 2nd-quantized approach, and its relation to Feynman diagrams.
- This book will drive the more mathematically inclined crazy, as the author admits, it makes very little attempt at rigour, and is very uncareful. He exchanges orders of limits willy-nilly, and often is not even clear about what sort of limiting process is taking place. There is not discussion of functional integration measures, or convergence, and there is very little justification provided for regularization methods (actually the coverage of dimensional regularization is extremely sparce, and would have been unfollowable, had I not already known it).
General Comments:
- I think that, contrary to some of the previous reviews, that the first few chapters of the book (through 6) would be a good first exposure to quantum field theory. I think the reader would have a much better understanding of the theory. However, the rest of the book is quite advanced, and would not be good for the uninitialized.
- I think that in an effort to make his coverage thorough and abstracting his discussion from phenomenology, the author sacrificed some of the readability of the book. That being said, if you're serious about learning the subject, this is a good resource.
Brilliant.......2006-09-15
Weinberg never disappoints the serious student of theoretical physics. There is no good reason to ignore perusing his texts.
Weinberg is a master expositor and creator of modern physics.
There simply is no good reason not to purchase his volumes.
superb book .......2006-08-16
in my opinion this should be one of the best books in qft.
Althought I've read jauch&rohrlich photons and electrons, p.ramond, itzykson, and ultimately, hatfield, Weinberg lead all of them for many heads. The features of this book are clarity, deepness, rigor, and authoritative treatment of all the topics. The discussion for a lagrangian versus hamiltonian formalism is lucid,and no finded in any other book. Group theory is applyied when is customary without cross over the physical implications. It contains a chapter devoted to scattering like no other book, wich is clear and explain concepts involved with "in" and "out" states(other of the lacks of many books of qft). Even the problems that contain are very well picked up, and solvable in most cases. I could't find any fault or mislead in what i read in this book, perhaps any skilled reader can find some. Even binding and typography are excellent, there is nothing more valuable for hardly 40$.
Reading for Rhetoric.......2006-03-31
Physics is usually a horribly taught subject, that is why most students avoid it. When it is effectively communicated, physics can be wonderful. This book represents the former. It is dense. The author is obviously a brilliant person; but, he is not a brilliant communicator. I've got a Master's in Physics and I was lost by the end of the second chapter. I have no doubt that the mathematics as presented are accurate; however, alone they fail to effectively communicate the substance of the topic to a mere mortal. Weinberg does not spend adequate time discussing the context, reality, or historical evolution of his ideas. I purchased all three volumes and, apparently, waisted my money.
I later purchased Roger Penrose's "The Road to Reality" and thoroughly enjoyed it. It was not an easy read either, but Penrose spent a significant amount of time recounting historical context, impact, and the 'reality' of his ideas.
Perfection, but advanced.......2006-01-10
This is one of the best written physics books to ever hit the market. However, it deals with an advanced topic and its not for the faint of heart or those without the proper background. Weinberg's writing style is remarkably clear. A historical introduction (which is very enlightening) is followed by a nice chapter on relatavistic quantum mechanics. Later chapters which I found very useful include a chapter titled "Quantum Fields and Antiparticles", where he introduces the Dirac formalism, and "The Feynman Rules", which is one of the best presentations on this topic I have come across. Chapters on the Lagrangian methods and path integrals are also good. I would strongly advise the reader to thoroughly study other quantum field theory books before tackling this one.
Also recommended (to get started): "Quantum Field Theory in a Nutshell"
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- Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists
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