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Messiah A. Quantum Mechanics (2 Volumes in 1)

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Messiah A. Quantum Mechanics (2 Volumes in 1)
New York: Dover Publications, 2017.– 712 p.
Converted from epub version (with OCR). Pages: 1152 (paperback), 803 (epub), 712 (pdf).
Это английский перевод французского оригинала. Русский перевод (twirpx): Мессиа А. Квантовая механика.
Review (Amazon.com):
" ... this great work ought to be mastered by every postgraduate research student in theoretical physics ... there is no other book like it." – Proceedings of the Physical Society (England)
Simple enough for students yet sufficiently comprehensive to serve as a reference for working physicists, this classic text initially appeared as a two-volume French edition and is now available in this convenient, all-in-one-book English translation. Formalism and its interpretation receive a detailed treatment in the first volume, starting with the origins of quantum theory and examinations of matter waves and the Schrodinger equation, one-dimensional quantized systems, the uncertainty relations, and the mathematical framework and physical content of formalism. An analysis of simple systems includes a look at the separation of variables, scattering problems and phase shifts, the Coulomb interaction, and the harmonic oscillator. Volume II begins with an exploration of symmetries and invariance, including a consideration of angular momentum, identical particles and the Pauli exclusion principle, invariance and conservation laws, and time reversal. Methods of approximation discussed include those involving stationary perturbations, the equation of motion, variational method, and collision theory. The final chapters review the elements of relativistic quantum mechanics, and each volume concludes with useful appendixes.
The book has been hailed for the clarity and coherence of its presentation, and its scrupulous attention to detail.
One customer review (Amazon.com):
Published in 1958, this book is still used as a reference in graduate classes in quantum mechanics. One property of older books on quantum theory that is missing in more modern treatments is the inclusion of the history behind the subject. A discussion of the historical origins of a physical theory is of great importance in the learning and the appreciation of the subject. The first chapter of the first volume of this work does that very well, for the author gives a detailed discussion of the issues and experiments that were arising in classical physics in the early years of the 20th century that gave birth to quantum theory. This is followed in chapter two by an introduction (with history) to matter waves and the Schroedinger equation. Both of these chapters are very effective in developing the physical intution behind the quantum theory, beset as it is with problems of interpretation and mathematical inconsistencies.
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 quantum 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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