QUANTUM MECHANICS

1 QUANTUM MECHANICS . A Paradigms Approach This page intentionally left blank QUANTUM MECHANICS . A Paradigms Approach David H. McIntyre Oregon State University with contributions from Corinne A. Manogue, Janet Tate and the Paradigms in Physics group at Oregon State University Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montr al Toronto Delhi Mexico City S o Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Publisher: Jim Smith Cover Design: Mark Ong Editorial Manager: Laura Kenney Manufacturing Buyer: Kathy Sleys Senior Project Editor: Katie Conley Manager, Rights and Permissions: Zina Arabia Assistant Editors.

2 Peter Alston and Steven Le Manager, Cover Visual Research &. Senior Marketing Manager: Kerry McGinnis Permissions: Karen Sanatar Managing Editor: Corinne Benson Printer and Binder: Courier, Westford Production Project Manager: Mary O'Connell Cover Printer: Courier, Westford Production Management and Composition: Cover Images: David H. McIntyre Element LLC. Copyright 2012 Pearson Education, Inc., publishing as Pearson Addison-Wesley, 1301 Sansome St., San Francisco, CA 94111. All rights reserved. Manufactured in the United States of America.

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4 Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. Library of Congress Cataloging-in-Publication Data McIntyre, David H. QUANTUM MECHANICS : a paradigms approach / David H. McIntyre ; with contributions from Corinne A. Manogue, Janet Tate, and the Paradigms in Physics group at Oregon State University. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-321-76579-6. ISBN-10: 0-321-76579-6. 1. QUANTUM theory. 2. MECHANICS .

5 I. Manogue, Corinne A. II. Tate, Janet. III. Oregon State University. IV. Title. 2012. 2011039322. ISBN 10: 0-321-76579-6. ISBN 13: 978-0-321-76579-6. 1 2 3 4 5 6 7 8 9 10 CRW 16 15 14 13 12 11. Brief Contents 1 Stern-Gerlach Experiments 1. 2 Operators and Measurement 34. 3 Schr dinger Time Evolution 68. 4 QUANTUM Spookiness 97. 5 Quantized Energies: Particle in a Box 107. 6 Unbound States 161. 7 Angular Momentum 202. 8 Hydrogen Atom 250. 9 Harmonic Oscillator 275. 10 Perturbation Theory 312. 11 Hyper ne Structure and the Addition of Angular Momenta 355.

6 12 Perturbation of Hydrogen 382. 13 Identical Particles 410. 14 Time-Dependent Perturbation Theory 445. 15 Periodic Systems 469. 16 Modern Applications of QUANTUM MECHANICS 502. Appendices 529. Index 553. v This page intentionally left blank Contents Preface xiii Prologue xix 1 Stern-Gerlach Experiments 1. Stern-Gerlach Experiment 1. Experiment 1 5. Experiment 2 6. Experiment 3 7. Experiment 4 8. QUANTUM State Vectors 10. Analysis of Experiment 1 16. Analysis of Experiment 2 16. Superposition States 19. Matrix Notation 22. General QUANTUM Systems 25.

7 postulates 27. Summary 28. Problems 29. Resources 32. Activities 32. Further Reading 33. 2 Operators and Measurement 34. Operators, Eigenvalues, and Eigenvectors 34. Matrix Representation of Operators 37. Diagonalization of Operators 38. New Operators 41. Spin Component in a General Direction 41. Hermitian Operators 44. Projection Operators 44. Analysis of Experiments 3 and 4 47. Measurement 50. Commuting Observables 54. Uncertainty Principle 56. S2 Operator 57. Spin-1 System 59. vii viii Contents General QUANTUM Systems 62. Summary 63.

8 Problems 64. Resources 67. Activities 67. 3 Schr dinger Time Evolution 68. Schr dinger Equation 68. Spin Precession 72. Magnetic Field in the z-Direction 72. Magnetic Field in a General Direction 78. Neutrino Oscillations 84. Time-Dependent Hamiltonians 87. Magnetic Resonance 87. Light-Matter Interactions 92. Summary 93. Problems 94. Resources 96. Activities 96. Further Reading 96. 4 QUANTUM Spookiness 97. Einstein-Podolsky-Rosen Paradox 97. Schr dinger Cat Paradox 102. Problems 105. Resources 106. Further Reading 106. 5 Quantized Energies: Particle in a Box 107.

9 Spectroscopy 107. Energy Eigenvalue Equation 110. The Wave Function 112. In nite Square Well 119. Finite Square Well 128. Compare and Contrast 133. Wave Function Curvature 133. Nodes 135. Barrier Penetration 135. Inversion Symmetry and Parity 136. Orthonormality 136. Completeness 137. Superposition States and Time Dependence 137. Modern Application: QUANTUM Wells and Dots 146. Asymmetric Square Well: Sneak Peek at Perturbations 147. Fitting Energy Eigenstates by Eye or by Computer 150. Qualitative (Eyeball) Solutions 150. Contents ix Numerical Solutions 151.

10 General Potential Wells 154. Summary 154. Problems 156. Resources 159. Activities 159. Further Reading 160. 6 Unbound States 161. Free Particle Eigenstates 161. Energy Eigenstates 161. Momentum Eigenstates 163. Wave Packets 168. Discrete Superposition 168. Continuous Superposition 171. Uncertainty Principle 176. Energy Estimation 180. Unbound States and Scattering 181. Tunneling Through Barriers 188. Atom Interferometry 192. Summary 197. Problems 197. Resources 201. Activities 201. Further Reading 201. 7 Angular Momentum 202. Separating Center-of-Mass and Relative Motion 204.