Mathematical Concepts of Quantum Mechanics
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the
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Universitext Series Editors: Sheldon Axler San Francisco State University Vincenzo Capasso Universita` degli Studi di Milano Carles Casacuberta Universitat de Barcelona Angus J. MacIntyre Queen Mary, University of London Kenneth Ribet University of California, Berkeley Claude Sabbah ´ CNRS, Ecole Polytechnique Endre S¨uli University of Oxford Wojbor A. Woyczynski Case Western Reserve University
Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, to very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext.
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Stephen J. Gustafson Israel Michael Sigal
Mathematical Concepts of Quantum Mechanics Second Edition
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Stephen J. Gustafson University of British Columbia Dept. Mathematics Vancouver, BC V6T 1Z2 Canada [email protected]
Israel Michael Sigal University of Toronto Dept. Mathematics 40 St. George Street Toronto, ON M5S 2E4 Canada [email protected]
ISBN 978-3-642-21865-1 e-ISBN 978-3-642-21866-8 DOI 10.1007/978-3-642-21866-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011935880 Mathematics Subject Classification (2010): 81S, 47A, 46N50 c Springer-Verlag Berlin Heidelberg 2011 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 to prosecution under the German Copyright Law. 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 protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Preface to the second edition Oneof the main goals motivating this new edition was to enhance the elementary material. To this end, in addition to some rewriting and reorganization, several new sections have been added (covering, for example, spin, and conservation laws), resulting in a fairly complete coverage of elementary topics. A second main goal was to address the key physic
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