E-Book Overview
This is the first of four volumes on quantum mechanics and quantum field theory. It is self-contained, and the only prerequisites are knowledge of integral calculus and partial differential equations, as well as Newton's mechanics of point masses. Each chapter is complemented by ten problems.
E-Book Content
Qwmtum Mechanics A Self-Conmined COUTSe Volwne 1 5P Rinlon Pre.. ·Quantum Mechanics A Self-Contained Course David ATKINSON Mahouton Norbert HOUNKONNOU Volume 1 5P Rinton Press Quantum Mechanics A Self-Contained Course This book is the frrst in a series of three volumes devoted to quantum mechanics and to quantum field theory. It is self-contained: the only prerequisites are a knowledge of integral calculus and partial differential equations, as well as Newton's mechanics of point masses. New subjects are developed in requisite detail at the various points where they are needed. The mathematics is at the same time explicit but kept in check, so that the reader does not get bogged down in annoying generalizations that might distract him or her from the physics. Each chapter is complemented by ten problems, one hundred in all, that are graded in difficulty, and the student is strongly advised to try them all before looking at the full solutions in the third volume. Visit Rinton Press on the World Wide Web at: http://www.rinton.com -3 90000 9 Quantum Mechanics A Self-Contained Course David ATKINSON Mahouton Norbert HOUNKONNOU Volume 1 Rinton Press, Inc. © 2001 Rinton Press, Inc. 12 Castleton Road Princeton, New Jersey 08540 USA All right reserved. No part of this book covered by the copyright hereon may be reproduced or used in any form or by any means-graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage and retrieval system - without permission of the publisher. Idea for cover design: Jeanne Peijnenburg Published by Rinton Press, Inc. Printed in the United State of America ISBN 1-58949-022-3 Preface This book is the first in a series of three volumes devoted respectively to (1) N onrelativistic Quantum Mechanics (2) Relativistic Quantum Field Theory (3) Problems and Solutions, in which the 200 exercises of the first two volumes are solved and discussed. These volumes are self-contained in the sense that the only prerequisites are a knowledge of integral calculus and partial differential equations, as well as Newton's mechanics of point masses. It is not necessary for the reader to know anything about the theory of distributions, Hilbert space or the special functions of mathematical physics. Nor is any knowledge of Lagrangian and Hamiltonian formalism assumed, for all these subjects are developed in requisite detail at the various points where they are needed. On the other hand, it would be helpful for the student to have followed an introductory course on quantum mechanics, to have some notion of what a wave-function is, and to have struggled with the Schrodinger equation in one spatial dimension. In this first volume, we have not made any attempt to cover all subjects of physical interest, but have made a choice appropriate for a course based on two hours of lectures and two hours of problem sessions during one undergraduate semester. Each chapter of this volume is complemented by ten problems, and the student is strongly advised to try them all by himself or herself before looking at our solutions in Volume 3. Physics cannot be learned just by reading or listening, but only by thinking, writing and worrying. The idea of writing a self-contained course originated with one of us (MNH). While the other (DA) was lecturing at the Institute of Mathematics and Physical Sciences of the National University of Benin in February 20