Quantum Mechanics For Physicists

One day in 1900, German physicist Max Planck told his son that he had made a breakthrough as important as Isaac Newton's discovery of the workings of the universe. Planck had reached the surprising conclusion that light behaves as if it is packaged in discrete amounts, or quanta, a seemingly simple observation that would lead to a powerful new field of physics called quantum mechanics.

The German edition of this book appeared in 1932 under the title "Die gruppentheoretische Methode in der Quantenmechanik". Its aim was, to explain the fundamental notions of the Theory of Groups and their Representations, and the application of this theory to the Quantum Mechanics of Atoms and Molecules. The book was mainly written for the benefit of physicists who were supposed to be familiar with Quantum Mechanics. However, it turned out that it was also used by. mathematicians who wanted to learn Quantum Mechanics from it. Naturally, the physical parts were too difficult for mathematicians, whereas the mathematical parts were sometimes too difficult for physicists. The German language created an additional difficulty for many readers. In order to make the book more readable for physicists and mathe­ maticians alike, I have rewritten the whole volume. The changes are most notable in Chapters 1 and 6. In Chapter t, I have tried to give a mathematically rigorous exposition of the principles of Quantum Mechanics. This was possible because recent investigations in the theory of self-adjoint linear operators have made the mathematical foundation of Quantum Mechanics much clearer than it was in t 932. Chapter 6, on Molecule Spectra, was too much condensed in the German edition. I hope it is now easier to understand. In Chapter 2-5 too, numerous changes were made in order to make the book more readable and more useful.

In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics. In view of this progress, this volume is very timely; it is the first text totally devoted to multiscale methods as applied to various areas of physics and to the relative developments in mathematics.

Quantum mechanics is a physical theory for objects of the microcosm, e.g. for atoms or electrons. It has proven itself so far, but leads to the fact that we have to grant properties and relations to these objects, which are neither compatible with our common sense nor with the concepts of classical physics. These peculiarities are presented and their significance for our cognitive faculty and for a world view is discussed.