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The cover was printed by Hamilton Printing Company. This book is printed on acid-free paper. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections or of the United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Rosewood Drive, Danvers, MA , , fax Quantum mechanics I Eugen Merzbacher.

Includes bibliographical references and index. ISBN cloth: alk. Quantum theory. M47 This book was written for such a course as a comprehensive introduction to the principles of quantum mechanics and to their application in the subfields of physics.

The first edition of this book was published in , the second in At that time there were few graduate-level texts available to choose from. While this new updated edition differs substantially from its predecessors, the underlying purpose has remained the same: To provide a carefully structured and coherent exposition of quantum mechanics; to illuminate the essential features of the theory without cutting corners, and yet without letting technical de- tails obscure the main storyline; and to exhibit wherever possible the common threads by which the theory links many different phenomena and subfields.

The reader of this book is assumed to know the basic facts of atomic and sub- atomic physics and to have been exposed to elementary quantum mechanics at the undergraduate level. Knowledge of classical mechanics and some familiarity with electromagnetic theory are also presupposed. My intention was to present a self- contained narrative, limiting the selection of topics to those that could be treated equitably without relying on specialized background knowledge.

The material in this book is appropriate for three semesters or four quarters. The first 19 chapters can make up a standard two-semester or three-quarter course on nonrelativistic quantum mechanics. The pace quick- ens here, and many mathematical steps are left to the exercises.

It would be pre- sumptuous to claim that every section of this book is indispensable for learning the principles and methods of quantum mechanics. Suffice it to say that there is more here than can be comfortably accommodated in most courses, and that the choice of what to omit is best left to the instructor.

Although my objectives are the same now as they were in the earlier editions, I have tried to take into account changes in physics and in the preparation of the students. Much of the first two-thirds of the book was rewritten and rearranged while I was teaching beginning graduate students and advanced undergraduates.

Since most students now reach this course with considerable previous experience in quan- tum mechanics, the graduated three-stage design of the previous editions-wave mechanics, followed by spin one-half quantum mechanics, followed in turn by the full-fledged abstract vector space formulation of quantum mechanics-no longer seemed appropriate.

In modifying it, I have attempted to maintain the inductive approach of the book, which builds the theory up from a small number of simple empirical facts and emphasizes explanations and physical connections over pure formalism.

Some introductory material was compressed or altogether jettisoned to make room in the early chapters for material that properly belongs in the first half of this course without unduly inflating the book. I have also added several new topics and tried to refresh and improve the presentation throughout. The Schrodinger equation is established, the prob- ability interpretation induced, and the facility for manipulating operators acquired. The principles of quantum mechanics, previously presented in Chapter 8, are now already taken up in Chapter 4.

Gauge symmetry, on which much of contemporary quantum field theory rests, is introduced at this stage in its most elementary form. This is followed by practice in the use of fundamental concepts Chapters 5, 6, and 7 , including two-by-two matrices and the construction of a one-dimensional version of the scattering matrix from symmetry principles.

Since the bra-ket notation is already familiar to all students, it is now used in these early chapters for matrix elements. The easy access to computing has made it possible to beef up Chapter 7 on the WKB method. In order to enable the reader to solve nontrivial problems as soon as possible, the new Chapter 8 is devoted to several important techniques that previously became available only later in the course: Variational calculations, the Rayleigh-Ritz method, and elementary time-independent perturbation theory.

A section on the use of nonorthogonal basis functions has been added, and the applications to molecular and condensed-matter systems have been revised and brought together in this chapter. The general principles of quantum mechanics are now the subject of Chapters 9 and Coherent and squeezed harmonic oscillator states are first encountered here in the context of the uncertainty relations.

Angular momentum and the nonre- lativistic theory of spherical potentials follow in Chapters 11 and Chapter 13 on scattering begins with a new introduction to the concept of cross sections, for col- liding and merging beam experiments as well as for stationary targets.

New features include a short account of Feynman path integration and a longer discussion of density operators, entropy and infor- mation, and their relation to notions of measurements in quantum mechanics.

All of this is then illustrated in Chapter 16 by the theory of two-state systems, 1.

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## Quantum Mechanics

The course is intended for graduate students in physics who have already had an introductory course in Modern Physics and Quantum Mechanics, at the level of the texts: Introduction to Quantum Mechanics, by David J. Griffiths, Prentice-Hall, Inc. For more course information, go here: Fall Physics Syllabus. Suggested Textbooks It is difficult to find one universally accepted textbook on quantum mechanics at the graduate level, as there are numerous approaches to its development. Here is the list of resources I will use in preparing lectures. My primary recommendation for a text where the conceptual development of the subject is pretty well described is the one by Messiah, I also like Schiff, but it seems to be out of print.

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## 0471887021 - Quantum Mechanics by Merzbacher, Eugen

The cover was printed by Hamilton Printing Company. This book is printed on acid-free paper. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections or of the United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Rosewood Drive, Danvers, MA , , fax Quantum mechanics I Eugen Merzbacher. Includes bibliographical references and index.