Wave Equations in Higher Dimensions
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an e
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Shi-Hai Dong
Wave Equations in Higher Dimensions
Shi-Hai Dong Escuela Superior de Física y Matemáticas Unidad Profesional Adolfo López Mateos Instituto Politécnico Nacional Edificio 9 Mexico DF 07738 Mexico [email protected]
ISBN 978-94-007-1916-3 e-ISBN 978-94-007-1917-0 DOI 10.1007/978-94-007-1917-0 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2011933232 © Springer Science+Business Media B.V. 2011 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: VTeX UAB, Lithuania Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
This book is dedicated to my wife Guo-Hua Sun and lovely children Bo Dong and Jazmin Yue Dong Sun.
Preface
This work will introduce the wave equations in higher dimensions at an advanced level addressing students of physics, mathematics and chemistry. The aim is to put the mathematical and physical concepts and techniques like the wave equations, group theory, generalized hypervirial theorem, the Levinson theorem, exact and proper quantization rules related to the higher dimensions at the reader’s disposal. For this purpose, we attempt to provide a comprehensive description of the wave equations including the non-relativistic Schrödinger equation, relativistic Dirac and Klein-Gordon equations in higher dimensions and their wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this field are the quantum mechanics and group theory. In fact, the author’s driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the wave equations in higher dimensions drawn from the teaching and research experience of the author since the literature is inundated with scattered articles in this field and to pave the reader’s way into this territory as rapidly as possible. We have made the effort to present the clear and understandable derivations and include the necessary mathematical steps so that the intelligent and diligent reader is able to follow the text with relative ease, in particular, when mathematically difficult material is presented. The author also embraces enthusiastically the potential of the LaTeX typesetting language to enrich the presentation of the formulas as to make the logical pattern behind the mathematics more transparent. In addition, any suggestions and criticism to improve the text are most welcome. It should be pointed out that the main effort to follow the text and master the material is left to the reader even though this book makes an effort to serve the reader as much as was
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