Quantum Mechanics (Physics)

Rating:
Summary: Definitely the classic to rush out and buy
Review: Albert Messiah's Quantum Mechanics has been used for the last 30 years or so by the most part of the people working in QM. Besides you can find it at the list of references of every decent text after its first appearence in 1962. At the University of Valencia, which holds some very nice theoretical physics groups, is given as a reference among Sakurai, Galindo-Pascual or Cohen- Tannaoudji, that also quote it.

The first volume deals with the formalism of operators and introduces quantum physics. The second one expands up to advanced topics such as tensorial irreductible operators and the Wigner-Eckard theorem. It fits to an advanced undergraduate or first graduate course, instructors should select the material as it is very comprehensive (about a thousand pages in the french two-volume Dunod edition).

It is an excellent choice if you are tired of those smart texts written with the goal of impressing colleagues. You can see clearly that Quantum Mechanics is a coherent physical theory, rather than a gift of heavens given to some divine genious.

Rating:
Summary: As an introduction this is a very good book
Review: For years I have come back again and again to the section on
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.

Rating:
Summary: Handy reference
Review: Messiah's writings have the same clarity as those of, say, Landau and Dirac. There are only two complaints one can make of this book - the first, it's too long. It seems as if nothing could be made shorter in this book, and yet it's about 1100 pages long! This leads up to the next complaint. Messiah chooses to begin developing QM from the wave equation and introduces Dirac's notation only around the 400th page - a big mistake, as anyone familiar with Dirac's notation can testify. One can, however, skip these 400 first pages and begin immediately with the formal treatment. All-in-all, a clear introduction well worth having, at least as a reference!

Rating:
Summary: Still suitable as a reference/historical introduction
Review: 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 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.

Rating:
Summary: Don't be afraid of the Size
Review: The book is huge, but that's why it includes more complete information about QM. It's easier to understand than some very popular standard and small textbooks. Both physics and math are balanced and self-contained. If you want books of the same quality and better presentation, maybe only Prof. Ta-You Wu's two books about QM would be.

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.

Rating:
Summary: Don't be afraid of the Size
Review: The book is huge, but that's why it includes more complete information about QM. It's easier to understand than some very popular standard and small textbooks. Both physics and math are balanced and self-contained. If you want books of the same quality and better presentation, maybe only Prof. Ta-You Wu's two books about QM would be.

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.

Rating:
Summary: A Good Thorough Book
Review: The book is thorough and covers all the topics in Quantum mechanics.The chapters follow just the way Q.M developed over the years.The reader would find it even more interesting if he/she has some background in Classical Mechanics because Messiah often refers to Hamilton-Jacobi equation, Action and Hamiltonian in general.

The book also develops Bra-Ket algebra in a very easy way, something I have not seen any other book.Messiah's way of treating scattering problems is quite different from that of the others. He doesn't make use of Green's Function but uses the wave-packet approach.

This books gets 3 stars because it's quite verbose. Messiah often gets stuck in explaining things over and over again(therefore the size of the book!). The drawback is that there are few problems per chapter and are quite difficult. This does not help the student gain confidence in the subject. The book assumes you are familiar with Electrodynamics.

Rating:
Summary: Monumental Treatise on Quantum Mechanics
Review: This books presents an extremely thorough treatment of both relativistic and non- relativistic quantum mechanics. All elements of the theory are treated in depth. Topics include wave mechanics, physical and mathematical content of the theory, simple systems, angular momentum, perturbation theory, and the Dirac equation. This book is probably not suitable for those learning quantum mechanics for the first time; however, I have found that it is very useful as a research reference.