242 solved problems of several degrees of difficulty in nonrelativistic Quantum Mechanics, ranging from the themes of the crisis of classical physics, through the achievements in the framework of modern atomic physics, down to the still alive, more intriguing aspects connected e.g. with the EPR paradox, the Aharonov--Bohm effect, quantum teleportation.
Problems in Quantum Mechanics Emilio d’Emilio • Luigi E. Picasso Problems in Quantum Mechanics with solutions Dr. Emilio d’Emilio Dipartimento di Fisica Università di Pisa, Italy Largo B. Pontecorvo 3 Pisa Italy
[email protected] Prof. Luigi E. Picasso Dipartimento di Fisica Università di Pisa, Italy Largo B. Pontecorvo 3 Pisa Italy
[email protected] ISSN 2038-5730 e-ISSN 2038-5765 ISBN 978-88-470-2305-5 e-ISBN 978-88-470-2306-2 DOI 10.1007/978-88-470-2306-2 Springer Milan Dordrecht Heidelberg London New York Library of Congress Control Number: 2011927609 © Springer-Verlag Italia 2011 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 microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the Italian Copyright Law in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the Italian Copyright Law. 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. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface This book stems from the experience the authors acquired by teaching Quantum Mechanics over more than two decades. The necessity of providing students with abundant and understandable didactic material – i.e. exercises and problems good for testing “in real time” and day by day their comprehension and mastery of the subject – confronted the authors with the necessity of adapting and reformulating the vast number of problems available from the final examinations given in previous years. Indeed those problems, precisely because they were formulated as final exam problems, were written in a language appropriate for the student who is already a good step ahead in his preparation, not for the student that, instead, is still in the “middle of the thing”. Imagining that the above necessity might be common to colleagues from other Departments and prompted also by the definite shortage, in the literature, of books written with this intent, we initially selected and ordered the 242 problems presented here by sticking to the presentation of Quantum Mechanics given in the textbook “Lezioni di Meccanica Quantistica” (ETS, Pisa, 2000) by one of us (LEP). Over time, however, our objective drifted to become making the present collection of problems more and more autonomous and independent of any textbook. It is for this reason that certain technical subjects – as e.g. the variational method, the virial theorem, selection rules etc. – are exposed in the form of problems and subsequently taken advantage of in more standard problems devoted to applications. The present edition – the first in English – has the advantage over the Italian one [“Problemi di Meccanica Quantistica” (ETS