Advanced University Physics Second Edition Advanced University Physics Second Edition Mircea S Rogalski Instituto Superior Técnico, Portugal Stuart B Palmer University of Warwick, UK Boca Raton London New York Singapore Cover photograph of a Wigner function plot courtesy of The University of Nottingham School of Physics and Astronomy. Published in 2006 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2006 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 1-58488-511-4 (Hardcover) International Standard Book Number-13: 978-1-58488-511-5 (Hardcover) Library of Congress Card Number 2005045510 This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Rogalski, Mircea S. Advanced university physics / by Mircea S. Rogalski and Stuart B. Palmer.-- 2nd ed. p. cm. Palmer's name appears first on earlier edition. Includes bibliographical references and index. ISBN 1-58488-511-4 (alk. paper) 1. Physics--Textbooks. I. Palmer, Stuart B. II. Title. QC21.3.P35 2005 530--dc22 2005045510 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com Taylor & Francis Group and the CRC Press Web site at is the Academic Division of T&F Informa plc. http://www.crcpress.com CONTENTS Preface xiii Chapter 1 INTRODUCTION 1 1.1. SI Units 1 1.2. Dimensional Analysis 3 1.3. Fundamental Physical Constants 9 Chapter 2 PRINCIPLES OF NEWTONIAN MECHANICS 11 2.1. Newton's Laws of Motion 11 2.2. Conservation of Momentum 23 2.3. Conservation of Energy 24 PROBLEMS 28 Chapter 3 ANGULAR MOMENTUM 40 3.1. Conservation of Angular Momentum 40 3.2. Motion under a Central Force 42 3.3. Kepler's Problem 47 3.4. Kepler's Laws 50 PROBLEMS 53 Chapter 4 PRINCIPLES OF SPECIAL RELATIVITY 65 4.1. Postulates of Special Relativity 65 4.2. The Lorentz Transformation 67 4.3. Spacetime Diagrams 73 4.4. Relativistic Invariance 77 PROBLEMS 81 Chapter 5 RELATIVISTIC LAWS OF MOTION 85 5.1. Relativistic Momentum and Energy 85 5.2. The Relativistic Equation of Motion 89 5.3. The Equivalence Principle 93 PROBLEMS 97 vi CONTENTS Chapter 6 CONTINUUM MECHANICS 105 6.1. Strain in a Continuum 105 6.2. Stress in a Continuum 109 6.3. Elastic Solids 113 6.4. Fluid Mechanics 116 PROBLEMS 121 Chapter 7 THE LAWS OF THERMODYNAMICS 129 7.1. Zeroth Law of Thermodynamics 129 7.2. First Law of Thermodynamics 132 7.3. Second Law of Thermodynamics 135 PROBLEMS 141 Chapter 8 THERMODYNAMIC FUNCTIONS 149 8.1. Clausius's Theorem 149 8.2. Entropy 151 8.3. Thermodynamic Potentials 153 8.4. Hydrostatic Systems 157 8.5. Heat Capacities 160 PROBLEMS 162 Chapter 9 PERFECT AND REAL GASES 168 9.1. Perfect Gas Laws 168 9.2. Thermodynamic Functions of a Perfect Gas 172 9.3. van der Waals Gas 175 PROBLEMS 180 Chapter 10 PHASE TRANSITIONS 187 10.1. Equilibrium Between Phases 187 10.2. First Order Phase Transitions 190 10.3. Higher Order Phase Transitions 192 10.4. The Phase Rule 193 10.5. Third Law of Thermodynamics 195 PROBLEMS 198 Chapter 11 ELECTROSTATICS 204 11.1. Electric Field 204 11.2. Electrostatic Potential 208 11.3. Polarization 213 11.4. Electrostatic Energy 216 PROBLEMS 218 CONTENTS vii Chapter 12 MAGNETIC INDUCTION 227 12.1. Current Flow 227 12.2. Magnetic Effects 231 12.3. Magnetic Vector Potential 239 PROBLEMS 242 Chapter 13 MAGNETIC FIELDS 247 13.1. Magnetization 247 13.2. Faraday's Law 252 13.3. Energy in Magnetic Fields 257 PROBLEMS 259 Chapter 14 MAXWELL'S EQUATIONS 265 14.1. Maxwell's Field Equations 265 14.2. Electromagnetic Energy 270 14.3. Potential Equations 273 PROBLEMS 276 Chapter 15 WAVE EQUATIONS 280 15.1. Equation of Wave Motion 280 15.2. Elastic Waves on a String 284 15.3. Sound Waves in Fluids 288 15.4. Electromagnetic Waves in Isotropic Dielectrics 292 PROBLEMS 295 Chapter 16 WAVE PROPAGATION 300 16.1. Harmonic Waves 300 16.2. Wave Propagation in Three Dimensions 304 16.3. Stationary Waves 309 16.4. Continuous Waves 313 16.5. Wave Dispersion 315 PROBLEMS 317 Chapter 17 WAVE ENERGY 326 17.1. Energy Density 326 17.2. Energy Flow 329 17.3. Wave Momentum 334 17.4. Attenuation of Waves 336 17.5. Wave Energy at an Interface 338 PROBLEMS 341 Chapter 18 INTERFERENCE 348 18.1. Interference of Two Monochromatic Waves 348 viii CONTENTS 18.2. Interference with Multiple Beams 354 PROBLEMS 359 Chapter 19 DIFFRACTION 366 19.1. Diffraction of Scalar Waves 366 19.2. The Linear Approximation of Diffraction 370 19.3. The Diffraction Grating 376 PROBLEMS 379 Chapter 20 POLARIZATION 387 20.1. The Transverse Nature of Electromagnetic Waves 387 20.2. Intensity of Electromagnetic Waves 390 20.3. The State of Polarization 393 20.4. Alternative Descriptions of Polarization 401 PROBLEMS 404 Chapter 21 REFLECTION AND REFRACTION 411 21.1. Electromagnetic Waves at an Interface 411 21.2. Fresnel's Equations 414 PROBLEMS 422 Chapter 22 WAVES IN ANISOTROPIC MEDIA 429 22.1. The Plane Wave Equation 429 22.2. Optical Anisotropic Media 433 22.3. Ray and Phase Velocity 437 PROBLEMS 441 Chapter 23 ABSORPTION AND DISPERSION 450 23.1. Optical Properties of Conducting Media 450 23.2. Origin of Complex Constitutive Parameters 457 PROBLEMS 463 Chapter 24 GENERALIZED MECHANICS 468 24.1. d'Alembert's Principle 468 24.2. Hamilton's Principle 471 24.3. Lagrange's Equations 473 24.4. The Canonical Equations 475 24.5. The Poisson Brackets 478 24.6. The Hamilton-Jacobi Equation 480 PROBLEMS 483 CONTENTS ix Chapter 25 PRINCIPLES OF STATISTICAL MECHANICS 490 25.1. Liouville's Theorem 490 25.2. Basic Statistical Assumptions 494 25.3. Boltzmann's Principle 498 25.4. Microcanonical Ensemble 504 25.5. Canonical Ensemble 506 25.6. Grand Canonical Ensemble 511 PROBLEMS 515 Chapter 26 STATISTICAL THERMODYNAMICS 522 26.1. Equipartition Theorem 522 26.2. Statistics of the Perfect Gas 525 26.3. The Maxwell-Boltzmann Distribution Law 529 26.4. The Gibbs Paradox 534 PROBLEMS 538 Chapter 27 THERMAL RADIATION 544 27.1. Thermodynamics of Radiation 544 27.2. Statistics of Radiation 549 27.3. Planck's Radiation Formula 553 PROBLEMS 556 Chapter 28 WAVE MECHANICS 561 28.1. The Corpuscular Nature of Radiation 561 28.2. The Old Quantum Theory 563 28.3. The Wave Nature of Particles 569 28.4. The Uncertainty Principle 573 PROBLEMS 575 Chapter 29 POSTULATES OF QUANTUM MECHANICS 581 29.1. Postulate 1: Wave Functions 581 29.2. Postulate 2: Operators 584 29.3. Postulate 3: Eigenvalues 587 29.4. Postulate 4: Commutation Relations 591 PROBLEMS 595 Chapter 30 THE SCHRÖDINGER PICTURE 601 30.1. Postulate 5: The Time-Dependent Schrödinger Equation 601 30.2. The Time-Independent Schrödinger Equation 604 30.3. Unbound States. Probability Current Density 606 30.4. Bound States. The Harmonic Oscillator 609 PROBLEMS 613