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Quantum Mechanics: Two Volumes Bound As One
- ISBN-100486409244
- ISBN-13978-0486409245
- PublisherDover Publications
- Publication dateJune 22, 2017
- LanguageEnglish
- Dimensions5.25 x 2 x 8.5 inches
- Print length1152 pages
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Product details
- Publisher : Dover Publications (June 22, 2017)
- Language : English
- Paperback : 1152 pages
- ISBN-10 : 0486409244
- ISBN-13 : 978-0486409245
- Item Weight : 2.5 pounds
- Dimensions : 5.25 x 2 x 8.5 inches
- Best Sellers Rank: #2,464,228 in Books (See Top 100 in Books)
- #2,478 in Physics (Books)
- Customer Reviews:
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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.
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This isn't a book for undergraduates. I think it will mainly appeal to those such as myself, who already know quite a bit about quantum mechanics and are trying to gain a mastery of the subject. Not all in one go, of course: this book looks like it requires a good few years of off-and-on reading to adequately digest. It also functions as a superb reference text. Almost everything you'll ever want to know about quantum mechanics is contained in these pages (with a few bothersome absences, e.g. Feynman path integrals).
The level of detail here is very high. (For instance, angular momentum isn't given a substantial discussion until the beginning of the second volume.) Many of the problems are intriguing, but don't expect the book to provide any solutions or hints -- because it doesn't. Of special interest is the last part of the second volume, which discusses the Dirac equation in considerable depth, and provides the equivalent of an introductory course on relativistic quantum mechanics. The final chapter, devoted to radiation theory, is extremely useful, providing a bridge to quantum field theory, and showing how to solve a bunch of physically interesting problems in radiation theory without having to invoke the usual quantum electrodynamics.
だからといって値段が安いし、中身は同じであるのだから、英語の勉強も兼ねてチャレンジしてみるのもいいだろう。
だけど全部綺麗に読むのは大変かもしれない。
しかしメシアの本は非常によくまとまっているので、辞書代わりに使うと言う手もある。
貧乏学生が英語のトレーニングに読むにはもってこいかもしれない。
だけどあまりの分厚さに驚くかもしれない....




