Mathematical Methods in Physics Distributions, Hilbert Space Operato
The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The author
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Editors-in-chief Anne Boutet de Monvel, Université Paris VII UFR de Mathematiques, Paris CX 05, France Gerald Kaiser, Center for Signals and Waves, Portland, Oregon, USA Editorial Board C. Berenstein, University of Maryland, College Park, USA Sir M. Berry, University of Bristol, UK P. Blanchard, University of Bielefeld, Germany M. Eastwood, University of Adelaide, Australia A.S. Fokas, University of Cambridge, UK F. W. Hehl, University of Cologne, Germany and University of Missouri-Columbia, USA D. Sternheimer, Université de Bourgogne, Dijon, France C. Tracy, University of California, Davis, USA
For further volumes: http://www.springer.com/series/4813
Philippe Blanchard • Erwin Brüning
Mathematical Methods in Physics Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics Second Edition
Philippe Blanchard Abt. Theoretische Physik Universität Bielefeld Fak. Physik Bielefeld Germany
ISSN 1544-9998 Progress in Mathematical Physics ISBN 978-3-319-14044-5 DOI 10.1007/978-3-319-14045-2
Erwin Brüning School of Mathematics, Statistics, and Computer Science University of KwaZulu-Natal Durban South Africa
ISSN 2197-1846 (electronic) ISBN 978-3-319-14045-2 (eBook)
Library of Congress Control Number: 2015931210 Mathematics Subject Classification (MSC): 46-01, 46C05, 46F05, 46N50, 47A05, 47L90, 49-01, 60E05, 81Q10 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2003, 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to the memory of Yurko Vladimir Glaser and Res Jost, mentors and friends
Preface to the Second Edition
The first edition of this book was published in 2003. Let us first thank everyone who, over the past 11 years, has provided us with suggestions and corrections for improving this first edition. We are extremely grateful for this help. The past decade has brough
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