F.Schwabl Advanced Quantum Mechanics Third Edition Springer
Professor Dr.Franz Schwabl 7 Garching.Germany E-mail:schwabl@physik.tu-muenchen.de Title of the original German edition:Quantenmechanik fur Fortgeschrittene(QM I) Library of Congress Control Number:2005928641 ISBN-10 3-540-25901-5 3rd ed.Springer Berlin Heidelberg New York ISBN-13 978-3-540-25901-0 3rd ed.Springer Berlin Heidelberg New York ISBN 3-540-40152-0 and ed.Springer-Verlag Berlin Heidelberg New York ze in data banks.Duplication of Springer is a part of Springer Science+Business Media springeronline.com Springer-Verlag Berlin Heidelberg9, Printed in The Netherlands The use of general descriptive nam Printed on acid-free paper6//YL531
Professor Dr. Franz Schwabl Physik-Department Technische Universit¨at Munchen ¨ James-Franck-Strasse 85747 Garching, Germany E-mail: schwabl@physik.tu-muenchen.de Translator: Dr. Roginald Hilton Dr. Angela Lahee Title of the original German edition: Quantenmechanik für Fortgeschrittene (QM II) (Springer-Lehrbuch) ISBN 3-540-67730-5 © Springer-Verlag Berlin Heidelberg 2000 Library of Congress Control Number: 2005928641 ISBN-10 3-540-25901-5 3rd ed. Springer Berlin Heidelberg New York ISBN-13 978-3-540-25901-0 3rd ed. Springer Berlin Heidelberg New York ISBN 3-540-40152-0 2nd ed. Springer-Verlag Berlin Heidelberg New York 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 for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 1999, 2004, 2005 Printed in The Netherlands 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: A. Lahee and F. Herweg EDV Beratung using a Springer TEX macro package Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: design & production GmbH, Heidelberg Printed on acid-free paper 56/3141/YL 5 4 3 2 1 0
The true physics is that which will,one day achieve the inclusion of man in his whole in a coherent picture of the world. Pierre Teilhard de Chardin To my daughter Birgitta
The true physics is that which will, one day, achieve the inclusion of man in his wholeness in a coherent picture of the world. Pierre Teilhard de Chardin To my daughter Birgitta
Preface to the Third Edition In the new edition,supplements,additional explanations and cross references have been added at numerous places,including new formulations of the prob- lems.Fig res have been redra wn and the lay out has been improved.in all additions I have intended to cha ct c lenweber.It was a pleasure to work with Dr.R.Hilton,in order to convey the spirit and the subtleties of the German text into the English translation. Also,I wish to thank Prof.U.Tauber for occasional advice.Special thanks go to them and to Mrs.Jorg-Muiller for general supervision.I would like to thank all colleagues and students who have made suggestions to improve the book,as well as the publisher,Dr.Thorsten Schneider and Mrs.J.Lenz for the excellent cooperation. Munich,May 2005 F.Schwabl
Preface to the Third Edition In the new edition, supplements, additional explanations and cross references have been added at numerous places, including new formulations of the problems. Figures have been redrawn and the layout has been improved. In all these additions I have intended not to change the compact character of the book. The proofs were read by E. Bauer, E. Marquard–Schmitt and T. Wollenweber. It was a pleasure to work with Dr. R. Hilton, in order to convey the spirit and the subtleties of the German text into the English translation. Also, I wish to thank Prof. U. T¨auber for occasional advice. Special thanks go to them and to Mrs. J¨org-M¨uller for general supervision. I would like to thank all colleagues and students who have made suggestions to improve the book, as well as the publisher, Dr. Thorsten Schneider and Mrs. J. Lenz for the excellent cooperation. Munich, May 2005 F. Schwabl
Preface to the First Edition This textbook deals with advanced topics in the field of quantum mechanics mater whichissnda ondpi tum mechanic. into three parts:I -Body Systems,II.Relat vistic Wave Equations,and III.Relativistic Fields.The text is written in such a way as to attach impor tance to a rigorous presentation while,at the same time,requiring no prior knowledge,except in the field of basic quantum mechanics.The inclusion of all mathematical steps and full presentation of intermediate calculations ensures ease of understanding.A number of problems are included at the end of each chapter Sections or parts thereof that can be omitted in a first emarked with a star,a nd subsidia emarks sma pri It is not necessary have read P works in the literature are given whenever it is felt they serve a useful pur pose.These are by no means complete and are simply intended to encourage further reading.A list of other textbooks is included at the end of each of the three parts. In contrast to Quantum Mechanics I.the present book treats relativistic phenomena,and classical and relativistic quantum fields. Part Iin oduces the forr of s ems that nd quntization and a applies this t can be e described using s mple methods These incl tron ga sand excit in weakly interacting Bose gases.The basic properties of the correlation and response functions of many-particle systems are also treated here. The second part deals with the Klein-Gordon and Dirac equations.Im- portant aspects,such as motion in a Coulomb potential are discussed,and particular attention is paid to symmetry properties. The third part presents Noether's theorem,the quantization of the Klein- Gordon Dira and adiatio n fields,and the tatistics the n.The final interac rix theory, heorem,Feynman rules,a few simple proces scattering and scattering,and basic aspects of radiative corrections are discussed
Preface to the First Edition This textbook deals with advanced topics in the field of quantum mechanics, material which is usually encountered in a second university course on quantum mechanics. The book, which comprises a total of 15 chapters, is divided into three parts: I. Many-Body Systems, II. Relativistic Wave Equations, and III. Relativistic Fields. The text is written in such a way as to attach importance to a rigorous presentation while, at the same time, requiring no prior knowledge, except in the field of basic quantum mechanics. The inclusion of all mathematical steps and full presentation of intermediate calculations ensures ease of understanding. A number of problems are included at the end of each chapter. Sections or parts thereof that can be omitted in a first reading are marked with a star, and subsidiary calculations and remarks not essential for comprehension are given in small print. It is not necessary to have read Part I in order to understand Parts II and III. References to other works in the literature are given whenever it is felt they serve a useful purpose. These are by no means complete and are simply intended to encourage further reading. A list of other textbooks is included at the end of each of the three parts. In contrast to Quantum Mechanics I, the present book treats relativistic phenomena, and classical and relativistic quantum fields. Part I introduces the formalism of second quantization and applies this to the most important problems that can be described using simple methods. These include the weakly interacting electron gas and excitations in weakly interacting Bose gases. The basic properties of the correlation and response functions of many-particle systems are also treated here. The second part deals with the Klein–Gordon and Dirac equations. Important aspects, such as motion in a Coulomb potential are discussed, and particular attention is paid to symmetry properties. The third part presents Noether’s theorem, the quantization of the Klein– Gordon, Dirac, and radiation fields, and the spin-statistics theorem. The final chapter treats interacting fields using the example of quantum electrodynamics: S-matrix theory, Wick’s theorem, Feynman rules, a few simple processes such as Mott scattering and electron–electron scattering, and basic aspects of radiative corrections are discussed