science education information book reviewsQuantum Mechanicsan introduction
Walter Greiner
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Professor Dr. Walter Greiner is the author of a series of books on theoretical physics that are based on his lectures at the Institute of Theoretical Physics of the Goethe University at Frankfurt, Germany. His books have been translated into several languages, of which the English version is published by the Springer Verlag. The quantum part especially has become popular throughout the world, so it has become something of a cliché to praise Greiner's texts, but praise is nevertheless in order. The most natural pedagogue in physics in probably Lev Landau, but if I had to choose between the Landau series and the Greiner series, I would choose the latter, not just because of it's greater modernity (Landau died in 1968, with his co-workers keeping the series current), but especially for the exceptional practical use that the Greiner series has. Greiner is not such an original thinker as Landau and most of his books follow the conventional rules on how to write a text on a particular subject in physics, but within this conventional framework he formulates his material like no other author. What most readers notice immediately is the clarity of the mathematics. While some authors seem to think they are helping the student by cutting corners in terms of mathematical rigor and others employ an overly direct style of mathematics that is typical of physicists, Greiner is able to present his mathematics in much the same style as the better pure mathematics authors do, without ever obscuring it's physical relevance.
Quantum Mechanics for instance, has "mathematical supplements" (as he calls it) about special functions which are certainly more instructive than J.D. Jackson's popular sections on special functions in his Classical Electrodynamics. Greiner presents much of his material in the form of examples and worked exercises. One example says more than a thousand words, as the saying goes, if it weren't for the fact that there are only few authors that can write good examples. Often examples are written carelessly and are chosen poorly. Greiner however is a master at writing examples and it's remarkable how an example's title alone can raise your interest and make you see the relevance of it's subject. Interestingly Greiner's examples are not just about putting the theory into numbers, but in them he develops much of his text's theory. This coincides with the fact that his books are not rigidly organised, but he presents the elements of his teachings as it comes to him naturally, whether it be in the main text or in an example. Because of this lack of predictability it's often hard to find a particular subject while browsing (also because of the lacking index), but that is no more and no less the consequence of his superior didactic insight (and so a better index would be a plus).
The incomplete index does illustrate one of the downsides of the English translation of the series. Not only did the editor fail to spot a number of mistakes in the translation, but the series is somewhat notorious for it's large number of typos. The German version (published by Harri Deutsch) only shows a "normal" number of mistakes so the Springer Verlag isn't doing itself justice. However, all these errors are minor errors such as typing errors and simple algebraic errors and if you can't spot these easily then this book series isn't for you anyway. I've never been able to spot a true technical error in any of Greiner's books, neither on the mathematical nor on the physical side. Also, the English translation isn't exactly The King's English, but you get used that quickly and in no way does this interfere with the readability.
Quantum mechanics, an introduction is an very good for the student who has already had some education in foundations of quantum mechanics. Following the conventional "inductive method" Greiner hopes to impart the student with some intuition by opening the book with a chapter on classic experiments that that led to the creation of quantum mechanics. He quotes Auguste Compte: "To understand a science it so necessary to know it's history." However, the first word on science is often not the last word on science and good example is electrodynamics. By nature a relativistic subject it can only be presented in a "logically connected" way (as Landau put it) by presenting it in a relativistic setting. Historically however, non-relativistic electrodynamics preceded the relativistic version, so what is historical is not always entirely logical: researchers created a theory in one setting and then later discovered it's better understood in another. Of course any physics student must be aware of the fundamental experiments that led to quantum mechanics, but say that this knowledge really helps to understand quantum mechanics conceptually is probably an exaggeration. If anything, Greiner should have pointed out the differences between Bohr and Kramer's "Old Quantum Theory" and Heisenberg's version, as Messiah does so well in his "Quantum Mechanics, part I". All in all Greiner's book does not do much to help the student understand the conceptual foundations of quantum mechanics, so some previous education in quantum mechanics would be helpful. Once you are comfortable (more or less) with the quantum mechanical concepts, then Greiner's book is an exquisite text that is far more direct and to the point than most physics texts. In former days quantum mechanics was regarded as a graduate level subject, but many universities today elect to teach quantum mechanics at the undergraduate level, which often leads to making compromises on rigor. Greiner however, has the ability to present graduate level material in a way that is fit for undergraduate students without reducing the rigor and there it does fill a niche. If you have read and understood this book then you can safely say you are well primed and that you can move on to quantum mechanics at the graduate level, for which we recommend Greiner's texts Quantum Mechanics, Special Chapters and/or Quantum Mechanics Symmetries, which are even better than the Introduction.
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