Wolfgang Nolting - Theoretical Physics 6: Quantum Mechanics - Basics

Theoretical Physics 6 Wolfgang Nolting Theoretical Physics 6 Quantum Mechanics - Basics Wolfgang Nolting Inst. Physik Humboldt-Universitt zu Berlin Berlin, Germany ISBN 978-3-319-54385-7 ISBN 978-3-319-54386-4 (eBook) DOI 10.1007/978-3-319-54386-4 Library of Congress Control Number: 2016943655 Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microlms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication.

Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional afliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland General Preface The nine volumes of the series Basic Course: Theoretical Physics are thought to be text book material for the study of university level physics. They are aimed to impart, in a compact form, the most important skills of theoretical physics which can be used as basis for handling more sophisticated topics and problems in the advanced study of physics as well as in the subsequent physics research. The conceptual design of the presentation is organized in such a way that Classical Mechanics (volume 1) Analytical Mechanics (volume 2) Electrodynamics (volume 3) Special Theory of Relativity (volume 4) Thermodynamics (volume 5) are considered as the theory part of an integrated course of experimental and theoretical physics as is being offered at many universities starting from the rst semester. Therefore, the presentation is consciously chosen to be very elaborate and self-contained, sometimes surely at the cost of certain elegance, so that the course is suitable even for self-study, at rst without any need of secondary literature.

At any stage, no material is used which has not been dealt with earlier in the text. This holds in particular for the mathematical tools, which have been comprehensively developed starting from the school level, of course more or less in the form of recipes, such that right from the beginning of the study, one can solve problems in theoretical physics. The mathematical insertions are always then plugged in when they become indispensable to proceed further in the program of theoretical physics. It goes without saying that in such a context, not all the mathematical statements can be proved and derived with absolute rigor. Instead, sometimes a reference must be made to an appropriate course in mathematics or to an advanced textbook in mathematics. vi General Preface The mathematical interludes are of course necessary only in the rst volumes of this series, which incorporate more or less the material of a bachelor program. vi General Preface The mathematical interludes are of course necessary only in the rst volumes of this series, which incorporate more or less the material of a bachelor program.

In the second part of the series which comprises the modern aspects of theoretical physics, Quantum Mechanics: Basics (volume 6) Quantum Mechanics: Methods and Applications (volume 7) Statistical Physics (volume 8) Many-Body Theory (volume 9) , mathematical insertions are no longer necessary. This is partly because, by the time one comes to this stage, the obligatory mathematics courses one has to take in order to study physics would have provided the required tools. The fact that training in theory has already started in the rst semester itself permits inclusion of parts of quantum mechanics and statistical physics in the bachelor program itself. It is clear that the content of the last three volumes cannot be part of an integrated course but rather the subject matter of pure theory lectures. This holds in particular for Many-Body Theory which is offered, sometimes under different names, e.g., Advanced Quantum Mechanics , in the eighth or so semester of study. In this part, new methods and concepts beyond basic studies are introduced and discussed which are developed in particular for correlated many particle systems which in the meantime have become indispensable for a student pursuing a masters or a higher degree and for being able to read current research literature.

In all the volumes of the series Theoretical Physics , numerous exercises are included to deepen the understanding and to help correctly apply the abstractly acquired knowledge. It is obligatory for a student to attempt on his own to adapt and apply the abstract concepts of theoretical physics to solve realistic problems. Detailed solutions to the exercises are given at the end of each volume. The idea is to help a student to overcome any difculty at a particular step of the solution or to check ones own effort. Importantly these solutions should not seduce the student to follow the easy way out as a substitute for his own effort. At the end of each bigger chapter, I have added self-examination questions which shall serve as a self-test and may be useful while preparing for examinations.

I should not forget to thank all the people who have contributed one way or another to the success of the book series. The single volumes arose mainly from lectures which I gave at the universities of Muenster, Wuerzburg, Osnabrueck, and Berlin (Germany), Valladolid (Spain), and Warangal (India). The interest and constructive criticism of the students provided me the decisive motivation for preparing the rather extensive manuscripts. After the publication of the German version, I received a lot of suggestions from numerous colleagues for improvement, and this helped to further develop and enhance the concept and the performance of the series. In particular, I appreciate very much the support by Prof. A. A.

Ramakanth, a long-standing scientic partner and friend, who helped me in many respects, e.g., what concerns the checking of the translation of the German text into the present English version. General Preface vii Special thanks are due to the Springer company, in particular to Dr. Th. Schneider and his team. I remember many useful motivations and stimulations. I have the feeling that my books are well taken care of.

Berlin, Germany Wolfgang Nolting August 2016 Preface to Volume 6 The main goal of the present volume 6 ( Quantum Mechanics: Basics ) corresponds exactly to that of the total basic course in Theoretical Physics . It is thought to be accompanying textbook material for the study of university-level physics. It is aimed to impart, in a compact form, the most important skills of theoretical physics which can be used as basis for handling more sophisticated topics and problems in the advanced study of physics as well as in the subsequent physics research. It is presented in such a way that it enables self-study without the need for a demanding and laborious reference to secondary literature. For the understanding of the text it is only presumed that the reader has a good grasp of what has been elaborated in the preceding volumes. Mathematical interludes are always presented in a compact and functional form and practiced when they appear indispensable for the further development of the theory.