Definitions
Let ψ(r ) and ψ †(r ) be the field operators resulting by quantizing (second-quantization) the wave function (and its complex conjugate) corresponding to the Schrödinger equation. From now on we take ħ= 1, r ,t = x, and we omit any external potential; we
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Springer Series in Solid-State Sciences Editors: M. Cardona P. Fulde H.-J. Queisser Volume 1 Principles of Magnetic Resonance 2nd Edition By C. P. Slichter Volume 2
Introduction to Solid-State Theory By O. Made1ung
Volume 3 Dynamical Scattering of X-Rays in Crystals By Z. G. Pinsker Volume 4
Inelastic Electron Tunneling Spectroscopy Editor: T. Wolfram
Volume 5
Fundamentals of Crystal Growth I. Macroscopic Equilibrium and Transport Concepts By F. Rosenberger
Volume 6
Magnetic Flux Structures in Superconductors By R. P. Huebener
Volume 7 Green's Functions in Quantum Physics By E. N. Economou Volume 8 Solitons and Condensed Matter Physics Editors: A. R. Bishop and T. Schneider Volume 9
Photoferroelectrics By V. M. Fridkin
Volume 10 Phonon Dispersion Relations in Insulators By H. Bilz and W. Kress
E. N. Economou
Green's Functions in Quantum Physics With 49 Figures
Springer-Verlag Berlin Heidelberg GmbH 1979
Professor Eleftherios N. Economou, PhD Department of Physics, University of Virginia Charlottesville, VA 22901, USA Series Editors:
Professor Dr. Manuel Cardona Professor Dr. Peter Fulde Professor Dr. Hans-Joachim Queisser Max-Planck-Institut fUr Festkorperforschung Biisnauer Strasse 171, D-7000 Stuttgart 80, Fed. Rep. of Germany
ISBN 978-3-662-11902-0 ISBN 978-3-662-11900-6 (eBook) DOI 10.1007/978-3-662-11900-6 Softcover reprint of the hardcover 1st edition 1979 Library of Congress Cataloging in Publication Data. Economou, E. N., 1940-. Green's functions in quantum physics. (Springer series in solid-state sciences; v. 7). Bibliography: p. Includes index. 1. Green's functions. 2. Quantum theory. I. Title. II. Series. QC174.17.G68E25 530.1'2 78-21304 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law, where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.
c Springer-Verlag Berlin Heidelberg 1979
Originally published by Springer-Verlag Berlin Heidelberg New York in 1979. The use of 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. Offset printing: Zechnersche Buchdruckerei, Speyer. Bookbinding: J. Schliffer oHG, Griinstad!. 2153/3130-543210
Preface
This text grew out of a series of lectures addressed to solid-state experimentalists and graduate students beginning their research career in solidstate physics. The first part consisting of Chaps.l and 2 is a rather extensive mathematical introduction which covers the material about Green's functions usually included in a graduate course on mathematical physics. Emphasis is given to those topics which are of
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