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H Digitized by the Internet Archive 2010 in http://www.archive.org/details/quantummechanics02tomo QUANTUM MECHANICS VOLUME II NEW QUANTUM THEORY M A N T U Q^U MECHANICS VOLUME II NEW QUANTUM THEORY BY TOMONAGA SIN-ITIRO The Tokyo University of Education, Japan TRANSLATED FROM THE JAPANESE BY KOSHIBA ® 1966 JOHN WILEY & SONS, INC., NEW YORK (Interscicnce Publishers Division) Xo pari oj this book may be reproduced in fl».r form by print, photoprint, microtilm or any other means uithout written permission jrom the publisher THIS BOOK WAS ORIGINALLY PUBLISHED IN JAPANESE BY THE MISUZU PUBLISHING COMPANY, TOKYO PUBLISHERS: NORTH-HOLLAND PUBLISHING COMPANY. AMSTERDAM Sole distributors for U.S.A. and Canada INTERSCIENCE PUBLISHERS, a division of JOHN WILEY & SONS, INC., NEW YORK PRINTED IN rHE NETHERLANDS PREFACE Beginning with the wave theory of matter, this volume discusses the final solution of the wave-particle paradox. Unlike most existing textbooks, emphasis is placed upon the fimdamentally classical nature of wave theory which becomes a quantum theory only after the quantization process. Accordingly, de Broglie's equation describing the matter wave and Schrodinger's equation giving probability ampli- tude are discussed separately. As a general rule, the author has not hesitated to depart from the strict historical order of development of quantum mechanics, just as in \^olume I. If the reader gets the impression that in Volume II physics has been relegated to the background, this is largely due to the very mathematical nature of the theory itself. This impression may also due to the fact that, in order to keep the size of the book to reasonable limits, the applications of the theory to various physical prob- lems have been limited to those necessary for a proper understanding of the theory. However the author tried to interprete the mathematical formulations in physical terms as far as possible. In explaining the meaning of the concept of a quantum-mechanical object use is made of an analogy from the theory of relativity. This suffers from the drawback of requiring additional study for those without a reasonable command of relativity theory. However, it may be argued that, for a proper understanding of Nature in terms of the quantum, just as revolutionary a change in thinking is required as was entailed in comprehending relativistic Nature inwhichno absolute time and no absolute motion relative to ether are conceivable. In planning this work it was the intention of the author to make the volumes selfcontained so that readers could understand the subject-matter without reference to other sources. Regrettably, the theory of observation could not be included and interested readers are referred to standard books such as those ofNeumann andBohm*. The chapter on "Angular Momentum and Spin" has been inserted in the EngHsh version. By this addition, the second volume becomes a more complete book and also a theoretical basis is provided for the description of the atomic spectral terms discussed in Volume I. SiN-ITIRO TOMONAGA Tokyo, Japan July 1965. * J. von Neumann, Die Mathematische Grundlagen der Quantenmechanik. Berlin: Springer Verlag, 1932. D. Bohm. Quantum Theory. New York: Prentice-Hall Inc., 1951.