Observables
Observables are the quantities that can be experimentally measured in a given physical framework. In this chapter, we discuss the observables of quantum mechanics, as well as the notion of “quantizing” a classical theory.
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Springer-V erlag Berlin Heidelberg GmbH
Stephen J. Gustafson Israel Michael Sigal
Mathematical Concepts of Quantum Mechanics
Springer
Stephen]. Gustafson University of British Columbia Department of Mathematics Vancouver, BC V6T lZ2 Canada e-mail: [email protected]
Israel Michael Sigal University of Toronto Department ofMathematics Toronto, ON MSG 3C3 Canada e-mail: [email protected]
Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
Mathematics Subject Classification (2000): 81S, 47A, 46N50 ISBN 978-3-540-44160-1 ISBN 978-3-642-55729-3 (eBook) DOI 10.1007/978-3-642-55729-3 This work is subject to copyright. AII 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 vers ion, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. http://www.springer.de © Springer-Verlag Berlin Heidelberg 2003 Originally published by Springer-Verlag Berlin Heidelberg New York in 2003
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: design & production GmbH, Heidelberg Typeset by the authors using a Springer ID"JlX macro package Printed on acid-free paper
46/3142db- 5 43210
Preface
The first fifteen chapters of these lectures (omitting four to six chapters each year) cover a one term course taken by a mixed group of senior undergraduate and junior graduate students specializing either in mathematics or physics. Typically, the mathematics students have some background in advanced analysis, while the physics students have had introductory quantum mechanics. To satisfy such a disparate audience, we decided to select material which is interesting from the viewpoint of modern theoretical physics, and which illustrates an interplay of ideas from various fields of mathematics such as operator theory, probability, differential equations, and differential geometry. Given our time constraint, we have often pursued mathematical content at the expense of rigor. However, wherever we have sacrificed the latter, we have tried to explain whether the result is an established fact, or, mathematically speaking, a conjecture, and in the former case, how a given argument can be made rigorous.
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