Group Theory and 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 theor
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Editors S. S. Chern 1. L. Doob 1. Douglas,jr. A. Grothendieck E. Heinz F. Hirzebruch E. Hopf S. Mac Lane W. Magnus M. M. Postnikov W. Schmidt D. S. Scott K.Stein 1. Tits B.L. van der Waerden
Managing Editors
B. Eckmann
1. K. Moser
B. L. van der Waerden
Group Theory and Quantum Mechanics Corrected Printing With 10 Figures
Springer-Verlag Berlin Heidelberg New York 1980
Prof. Dr. B. L. van der Waerden Mathematisches Institut der Universitiit Ziirich
Translation of the German Original Edition: Die Grundlehren der mathematischen Wissenschaften Barid 37, Die Gruppentheoretische Methode in der Quantenmechanik. Publisher: Verlag von Julius Springer, Berlin 1932
AMS Subject Classification (1970) 81--{)2, 81 A 09, 81 A 78
ISBN-13:978-3-642-65862-4 e-ISBN-13:978-3-642-65860-0 DOl: 10.1007/978-3-642-65860-0
library of Congress Cataloging in Publication Data Waerden. Bartel Leenert van der. 1903. Group theory and quantum mechanics. (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Beriicksichtigung der Anwendungsgebiete. Bd. 214) Translation of Die gruppentheoretische Methode in der Quantenmechanik. Bibliography: p. I. Quantum theory. 2. Groups. Theory of. I. Title. II. Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen. Bd. 214) QC174.17.G7W3\3 530.1'2 74-\3914
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Preface
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 mathematicians 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 linea
