Relativistic Quantum Mechanics
In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics as well as classical relativistic mechanics appear as speci
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Hartmut M. Pilkuhn
Relativistic Quantum Mechanics Second Edition With 21 Figures
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Professor Hartmut M. Pilkuhn Universität Karlsruhe Institut für theoretische Teilchenphysik 76128 Karlsruhe, Germany e-mail: [email protected]
Library of Congress Control Number: 2005929195
ISSN 0172-5998 ISBN-10 3-540-25502-8 2nd ed. Springer Berlin Heidelberg New York ISBN-13 978-3-540-25502-4 2nd ed.Springer Berlin Heidelberg New York ISBN 3-540-43666-9 1st ed. Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2003, 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant probreak tective laws and regulations and therefore free for general use. Typesetting: Data conversion by LE-TeX Jelonek, Schmidt & Vöckler GbR Cover design: design & production GmbH, Heidelberg Printed on acid-free paper SPIN 11414094 55/3141/YL 5 4 3 2 1 0
Preface to the Second Edition
This edition includes five new sections and a third appendix. Most other sections are expanded, in particular Sects. 5.2 and 5.6 on hyperfine interactions. Section 3.8 offers an introduction to the important field of relativistic quantum chemistry. In Sect. 5.7, the coupling of the anomalous magnetic moment is needed for a relativistic treatment of the proton in hydrogen. It generalizes a remarkable feature of leptonium, namely the non-hermiticity of magnetic hyperfine interactions. In Appendix C, the explicit calculation of the expectation value of an operator which is frequently approximated by a delta-function confirms that the singularity of relativistic wave functions at the origin is correct. The other three new sections cover dominantly nonrelaticistic topics, in particular the quark model. The coupling of three electron spins (Sect. 3.9) provides also the basis for the three quark spins of baryons (Sect. 5.9). For less than four particles, direct symmetry arguments are simpler than the representions of the permutation group which are normally used in the literature. Another new topic of this edition is the confirmation of the E 2 -dependence of atomic equations by the relativistic energy conservation in radiative atomic transitions, according to the time-dependent perturbation theory of Sect. 5.4. In the quark model,
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