This course-tested book explains in detail the theory of linear Hilbert-space operators and their use in quantum physics. The central mathematical tool of the book is the spectral theory of self-adjoint operators; in order to make the exposition self-contained, selected topics of functional analysis are included. An introduction to the theory of operator sets and algebras is also presented. This mathematical material is then used for a systematic analysis of the operator structure of quantum theory. Logical building of the theory is discussed as well as its practical aspects, such as spectral properties of quantum mechanical Hamiltonians, scattering theory, and more.
The second edition was extended by two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography was amended by about 130 new items.
Theoretical and Mathematical Physics The series founded in 1975 and formerly (until 2005) entitled Texts and Monographs in Physics (TMP) publishes high-level monographs in theoretical and mathematical physics. The change of title to Theoretical and Mathematical Physics (TMP) signals that the series is a suitable publication platform for both the mathematical and the theoretical physicist. The wider scope of the series is reflected by the composition of the editorial board, comprising both physicists and mathematicians. The books, written in a didactic style and containing a certain amount of elementary background materials, bridge the gap between advanced textbooks and research monographs. They can thus serve as basis for advanced studies, not only for lectures and seminars at graduate level, but also for scientists entering a field of research. Editorial Board W. Beiglböck, Institute of Applied Mathematics, University of Heidelberg, Germany J.-P. Eckmann, Department of Theoretical Physics, University of Geneva, Switzerland H. Grosse, Institute of Theoretical Physics, University of Vienna, Austria M. Loss, School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA S. Smirnov, Mathematics Section, University of Geneva, Switzerland L. Takhtajan, Department of Mathematics, Stony Brook University, NY, USA J. Yngvason, Institute of Theoretical Physics, University of Vienna, Austria Jiˇrí Blank • Pavel Exner • Miloslav Havlíˇcek Hilbert Space Operators in Quantum Physics Second Edition ABC Miloslav Havlíˇcek Doppler Institute and Faculty of Nuclear Sciences and Physical Engineering Czech Technical University Trojanova 13 12000 Prague Czech Republic
[email protected]fi.cvut.cz Jiˇrí Blank† Charles University Prague Czechia Pavel Exner Doppler Institute Bˇrehová 7 11519 Prague and Nuclear Physics Institute Czech Academy of Sciences ˇ z near Prague 25068 Reˇ Czech Republic
[email protected] ISBN 978-1-4020-8869-8 e-ISBN 978-1-4020-8870-4 Library of Congress Control Number: 2008933703 All Rights Reserved c 2008 Springer Science + Business Media B.V. c 1993, first edition, AIP, Melville, NY No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com To our wives and daughters Preface to the second edition Almost fifteen