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Quantum Mathematical Physics Springer-Verlag Berlin Heidelberg Gmbh Quantum Mathematical Physics Springer-Verlag Berlin Heidelberg GmbH ONLINE LIBRARY Physics and Astronomy http://www.springer.de/phys/ Walter Thirring Quantum Mathematical Physics Atoms, Molecules and Large Systems Translated by Evans M. Harrell II Second Edition Corrected and Revised Second Printing with Bibliographic Additions With 63 Figures , Springer Walter Thirring Institute for Theoretical Physics University ofVienna Boltzmanngasse 5 1090 Vienna, Austria Title ofthe original German edition: Lehrbuch der Mathematischen Physik Band 3: Quantenmechanik von Atomen und Molekiilen Band 4: Quantenmechanik groBer Systeme © Springer-Verlag Wien 1979 Library of Congress Cataloging-in-Publication Data applied for. Die Deutsche Bibliothek- CIP-Einheitsaufnahme: Thirring, Walter: Quantum mathematical physics : atoms, molecules and large systems 1 Walter Thirring. Transl. by Evans M. Harrell.- 2.ed.- (Physics and astronomy online library) ISBN 978-3-642-07711-1 ISBN 978-3-662-05008-8 (eBook) DOI 10.1007/978-3-662-05008-8 Second Edition 2002 Corrected and Revised Second Printing, with Bibliographic Additions, 2003 ISBN 978-3-642-07711-1 This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concemed, specifically the rights oftranslation, reprinting, reu se 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 perrnitted only under the provisions ofthe German Copyright Law of September 9, 1965, in its current version, and perrnission 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 2002 Originally published by Springer-Verlag Berlin Heidelberg New York in 2002 Softcover reprint of the hardcover 2nd edition 2002 Volume 3 (now Part !) © Springer-Verlag New York, !ne. 1981 Volume 4 (now Part Il)© Springer-Verlag New York, !ne. 1983 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 Typesetting: Frank Herweg, Leutershausen Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper SPIN 10930298 55/3141/ba- 5 4 3 2 1 O Preface This edition combines the earlier two volumes on Quantum Mechanics of Atoms and Molecules and on Quantum Mechanics of Large Systems, thus including in a single volume the material for a two-semester course on quantum physics. Since this volume is already quite heavy, I could not include many new results which show how lively the subject is. I just want to mention that inequality (IV:4.1.l.1) has been sharpened by T. Weidl by a factor 2][ and the difficult problem 1 of (III:4.6) has been solved by A. Martin. I have to thank N. Ilieva for the devotion in preparing this new edition. Vienna, November 2001 Walter Thirring Preface to the Second Edition: Quantum Mechanics of Atoms and Molecules Ever since the first edition of this volume appeared in 1980 quantum statistical mechanics has florished. Innumerable results in many areas have been obtained and it would require a series of volumes to do justice to all of them. On the other hand the first edition was already rather crowded with many details so it would not be overburdened any more. Thus I added only one chapter on quantum ergodic theory where one can get the main notions across without too much pain. Nevertheless many subjects treated in the book had splendidely developed ever since and the only way out I could see is to add some recent references which the interested reader can consult. For helpful advice I am indebted to many colleagues in particular to E.H. Lieb and H. Namhofer. Furthermore I have to thank Z. Vakhnenko for resetting the complete book on the computer. Last but not least Nevena Ilieva took on the tedious task to fight with the program to get all the corrections across. We tried to do our best but if the reader still finds some faults, as I am sure he will, he might blame it onto the moods of the computer. Vienna, December 1999 Walter Thirring Preface to the First Edition: Quantum Mechanics of Atoms and Molecules In this third volume of A Course in Mathematical Physics I have attempted not simply to introduce axioms and derive quantum mechanics from them, but also to progress to relevant applications. Reading the axiomatic literature often gives one the impression that it largely consists of making refined axioms, thereby freeing physics from any trace of down-to-earth residue and cutting it off from simpler ways of thinking. The goal pursued here, however, is to come up with concrete results that can be compared with experimental facts. Everything else should be regarded only as a side issue, and has been chosen for pragmatic reasons. It is precisely with this in mind that I feel it appropriate to draw upon the most modem mathematical methods. Only by their means can the logical fabric of quantum theory be woven with a smooth structure; in their absence, rough spots would inevitably appear, especially in the theory of unbounded operators, where the details are too intricate to be comprehended easily. Great care has been taken to build up this mathematical weaponry as completely as possible, as it is also the basic arsenal of the next volume. This means that many proofs have been tucked away in the exercises. My greatest concern was to replace the ordinary calculations of uncertain accuracy with better ones having error bounds, in order to raise the crude manners of theoretical physics to the more cultivated level of experimental physics. The previous volumes are cited in the text as I and 11; most of the mathematical terminology was introduced in volume I. It has been possible to make only sporadic reference to the huge literature on the subject of this volume-the reader with more interest in its history is advised to consult the compendious work of Reed and Simon [3]. X Preface to the First Edition: Quantum Mechanics of Atoms and Molecules Of the many colleagues to whom lowe thanks for their help with the German edition, let me mention F. Gesztesy, H. Grosse, P. Hertel, M. and T. Hoffmann­ Ostenhof, H. Narnhofer, L. Pittner, A. Wehrl, E. Weimar, and, last but not least, F. Wagner, who has transformed illegible scrawls into a calligraphic masterpiece. The Englist translation has greatly benefited from the careful reading and many suggestions ofH. Grosse, H. Narnhofer, and particularly B. Simon. Vienna Walter Thirring Spring, 1981 Preface to the First Edition: Quantum Mechanics of Large Systems In this final volume I have tried to present the subject of statistical mechanics in accordance with the basic principles of the series. The effort again entailed follo­ wing Gustav Mahler's maxim, "Tradition = Schlamperei" (i.e., filth) and clearing away a large portion of this tradition-laden area. The result is a book with little in common with most other books on the subject. The ordinary perturbation-theoretic calculations are not very useful in this field. Those methods have never led to propositions of much substance. Even when perturbation series, which for the most part never converge, can be given some asymptotic meaning, it cannot be determined how close the nth order approxima­ tion comes to the exact result. Since analytic solutions of nontrivial problems are beyond human capabilities, for better or worse we must settle for sharp bounds on the quantities of interest, and can at most strive to make the degree of accuracy satisfactory. The last two decades have seen successful and beautiful treatments of many fundamental issues - I have in mind the ordering of the states (2.1), properties of the entropy (2.2), noncommutative ergodic theory (3.1), the proof of the existence of the thermodynamic functions (4.3), and the mathematical analysis of Thomas­ Fermi theory (4.1.2), which provides an understanding of the stability of matter. The day is surely not far off when most of the remaining holes in the conceptual structure of quantum statistical mechanics will have been filled in and the questions that are not satisfactorily answered today will be added to the list of achievements. The successful completion of this course of mathematical physics in a reasonable time required the fortunate conjunction of several circumstances. As with volume III, I had active support from several collaborators, and in particular I am greatly obliged to B. Baumgartner, H. Narnhofer, A. Pflug, and A. Wehrl. Countless other XII Preface to the First Edition: Quantum Mechanics of Large Systems colleagues have helped indirectly by coping with other time-consuming duties for me. The English edition has again greatly benefited from the critical reading of B. Simon. The working conditions at the University of Vienna were invaluable for the completion of this project. Last but not least, the frictionless collaboration of Springer-Verlag in Vienna and my secretary and calligrapher F. Wagner enabled the books to appear quickly and at a reasonable price. I am aware that the uncompromising way of mathematical physics is not the easiest. Yet I feel that it has been one of the greatest intellectual accomplishments of our era to cast the laws of Nature in a clear mathematical form with rigorously deducible consequences. No amount of labor is too high a price to have paid for this. Let me conclude by also acknowledging and expressing my thanks to the reader who has borne with me to the end of the course. Walter Thirring Contents Preface V Preface to the Second Edition: Quantum Mechanics of Atoms and Molecules VII Preface to the First Edition: Quantum Mechanics of Atoms and Molecules IX Preface to the First Edition: Quantum Mechanics of Large Systems XI Symbols Defined in the Text XV I Quantum Mechanics of Atoms and Molecules 1 1 Introduction 3 1.1 The Structure of Quantum Theory.
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