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Note that this is some kind of must-know book for quantum mechanics - at least over here in Europe. Many professors base their lectures on this book and recommend reading it for a better understanding of quantum mechanics because they don't have time to cover all the subjects covered in the book...
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It was very difficult to grasp in Latin (I've had a try on it),
not that much easy in the Motte facsimile translation (I can assure it), and the Cajori-Motte edition was only half modernized and otherwise flawed.
This edition, sponsored by I.B. Cohen (the Latin editor) gives us a fresh, modern English translation of the text, and -almost as thick- a guide to using and reading this all-important book, which is not -as everybody is aware- an easy reader. One word of caution: Newton was, of course, (pace Leibnitz) the discoverer of calculus, but he doesn't use it here, but "more geometrico"
rigorous proofs, much in the style of that other genius of all ages, Archimedes. If you need help grasping the contents and impact of this work, then you must get some book like DENSMORE, D., Newton's Principia: The Central Argument (other auxiliary books are commented in the Guide potion of the book I'm reviewing).
This book is a jewel. Just like the original works of Einstein, Maxwell, Heisenberg, Schroedinger and all those giants. Many of the ideas presented in the book were written for the first time in history and probably they are not organized in a didactic form. The person buying this book should not expect to find a clear textbook when originally it was not written for the layman, but for the expert scientific community of its time. Buy this book, sit back, scan through it, and enjoy a true piece of history.
The Principa is not an introductory calculus for the modern reader. It is written in Newton's own notational style. This style is different from the modern one, used in calculus today. The modern calculus notation system was devised by Leibniz. Newton's system of notation proved less useful than Leibniz's, and the better one has won out. Leibniz had independently discovered the calculus prior to the publication of Principia. Thus, Leibniz was not influenced by Newton's notational style. Leibniz's discovery of the calculus was made in secret on the continent several years after Newton had made his own secret discovery of it in Britain. Leibniz's work was published only after Newton's Principia was published. This led Newton to wrongly believe that his work had been stolen. An epic debate between the British and continental academies ensued with each side championing their man.
This book has enormous historical interest. For a person who is already educated in calculus, this book will take you to the source of the subject matter, the mouth of the Nile, so to speak. As for the scientific method, this is where it was conceived.
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field quantization and radiation theory.
I bought this at the same time I bought Weinberg's Cosmology.
I had many of the same unitary problems I had with that book.
If someone would just publish in simple cgs or mks units?
The U(1) electromagnetic gauge equations and the coverage of Maxwell and Dirac theory
are exceptional. I was a poor student who had to sell
his books back each semester to afford the next one.
I bought this book as a long term reference and
it has delivered not theorems but accessibility and understandability.
To develop this intuition further, the author discusses one-dimensional quantum systems in the next chapter. His remarks that these kinds of problems serve to develop the student's understanding and he also refers to the fact that several problems can be reduced to ones that resemble the one-dimensional Schroedinger equation. With the advent of exactly solved many-particle systems in one-dimension that were discovered after this book was published, the consideration of one-dimensional problems such as are included in this chapter is of even more importance. Most of the "standard problems" are discussed here, such as the potential step, the square well potential, and the square potential barrier. The author also does not hesitate to discuss the mathematical properties of the one-dimensional Schroedinger equation.
Chapter 4 is an overview of the statistical interpretation of quantum mechanics. The most interesting (and controversial) part of this chapter is the statistical interpretation of the Heisenberg uncertainly relations. The root-mean-square deviations are defined precisely, but the author does not want to take a stand on the consequences that this move can entail, namely that the product of the root-mean-square deviations of position and momentum must be greater than Planck's constant is a statistical statement only. It does not say what could happen in principle to individual measurements of the position and momentum.
The next four chapter discuss both the rigorous mathematical formalism behind quantum mechanics and its physical interpretation. The author's approach is pretty standard, but at times he feels the need to relax mathematical rigor, such as in the treatment of the Dirac delta "function". A proper treatment of this would entail bringing in some heavy guns from functional analysis, and the author is evidently hesitant to do this in a book at this level. His treatment of pure states and mixtures, namely that of quantum statistical mechanics is too short and could be excluded without detracting from the main points in these chapters. A connection with the classical is given via a discussion of Ehrenfest's theorem. Becuase chaos in classical mechanics was not known at the time of writing, the discussion here is now very out of date. Proving a version of Ehrenfest's theorem for such systems has to this date eluded researchers and has prohibited a sound formulation of "quantum chaos". The author does discuss the WKB approximation and shows how it can be used to study tunneling through a potential barrier. Path integral methods, known at the time of writing, but not very popular then, are not considered. And, in this treatment of the tensor product, he does not deal with the issue of entanglement of states, the latter being of enormous importance in current attempts to realize "quantum computation".
The last three chapters of volume 1 cover exact solution methods for the Schroedinger equation, such as the scattering of a central potential, the harmonic oscillator, and Coulomb scattering. Such problems are now dealt with much more efficiently with symbolic computer languages such as Mathematica and Maple. The properties of the special functions that arise in these solutions are easily understood with the use of these packages.
Volume 2 begins with a consideration of angular momentum in qunatum mechanics. The considerations of symmetry and conservation principles in this discussion are very important from a modern standpoint, permeating as they do in high energy physics and the goals of unification. The author does discuss briefly the issue of time reversibility in quantum mechanics. This issue has occupied the minds of hundreds of theorists, in attempting to elucidate the connection between statistical mechanics, with its "arrow of time", and quantum mechanics, which is invariant under time-reversal.
Perturbation methods are discussed extensively in this volume. But here again, from a modern standpoint these methods can be treated best by the use of symbolic programming languages. In addition, since the use of a computer in physics was somewhat limited at the time this book was written, there is no inclusion of numerical methods. Any textbook on quantum mechanics at this level in the 21st century should include a very detailed introduction to numerical methods so as to prepare the student early on to techniques that will be used more and more in the decades ahead. The use of the computer, with dramatically enhanced computational power, will be the tool that will bring about more fundamental discoveries in the quantum realm in this century, particularly in quantum many-body physics and condensed matter.
The last two chapters consider relativistic quantum mechanics and quantum field theory. Although the discussion is completely out-dated now, because of the current emphasis on functional methods, rather than canonical quantization as is done here, the discussion might be helpful as to gain insight as to why the canonical approach fell into disfavor.
Anyway, if you need only one book about QM, this is the best. It's a complete course for senior or graduate students. And it's cheaper.
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I just can't figure out Why it is so expensive. I believe I bought it 2 years ago by half the price. (First-hand). Anyway, a must have for every Physics student.
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This book is remarkable for its depth of appreciation for American cultural values by a foreigner who deserves his American citizenship more than most Americans! Highly recommended to all immigrant Americans who question the worth of American values and to Americans who seem to have forgotten.
Also it is fascinating for students of physics who are interested in turn-of-the-century electromagnetic science and for those who seek a glimpse of Columbia University in 1880s.