QUANTUM MECHANICS

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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 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 This publication is protected by Copyright. and permission should be obtained from the publisher prior to any prohibited reproduction storage in a retrieval system. or transmission in any form or by any means electronic mechanical photocopying recording or likewise To obtain. permission s to use material from this work please submit a written request to Pearson Education Inc Permissions. Department 1900 E Lake Ave Glenview IL 60025 For information regarding permissions call 847 486 2635. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks 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,Includes bibliographical references and index. ISBN 13 978 0 321 76579 6,ISBN 10 0 321 76579 6, 1 Quantum theory 2 Mechanics I Manogue Corinne A II Tate Janet. III Oregon State University IV Title,QC174 12 M3785 2012.
530 12 dc23,2011039322,ISBN 10 0 321 76579 6,ISBN 13 978 0 321 76579 6. www pearsonhighered com 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. 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. This page intentionally left blank,Preface xiii,Prologue xix.
1 Stern Gerlach Experiments 1,1 1 Stern Gerlach Experiment 1. 1 1 1 Experiment 1 5,1 1 2 Experiment 2 6,1 1 3 Experiment 3 7. 1 1 4 Experiment 4 8,1 2 Quantum State Vectors 10,1 2 1 Analysis of Experiment 1 16. 1 2 2 Analysis of Experiment 2 16,1 2 3 Superposition States 19. 1 3 Matrix Notation 22,1 4 General Quantum Systems 25.
1 5 Postulates 27,Summary 28,Problems 29,Resources 32. Activities 32,Further Reading 33,2 Operators and Measurement 34. 2 1 Operators Eigenvalues and Eigenvectors 34,2 1 1 Matrix Representation of Operators 37. 2 1 2 Diagonalization of Operators 38,2 2 New Operators 41. 2 2 1 Spin Component in a General Direction 41,2 2 2 Hermitian Operators 44.
2 2 3 Projection Operators 44,2 2 4 Analysis of Experiments 3 and 4 47. 2 3 Measurement 50,2 4 Commuting Observables 54,2 5 Uncertainty Principle 56. 2 6 S2 Operator 57,2 7 Spin 1 System 59,viii Contents. 2 8 General Quantum Systems 62,Summary 63,Problems 64. Resources 67,Activities 67,3 Schr dinger Time Evolution 68.
3 1 Schr dinger Equation 68,3 2 Spin Precession 72. 3 2 1 Magnetic Field in the z Direction 72,3 2 2 Magnetic Field in a General Direction 78. 3 3 Neutrino Oscillations 84,3 4 Time Dependent Hamiltonians 87. 3 4 1 Magnetic Resonance 87,3 4 2 Light Matter Interactions 92. Summary 93,Problems 94,Resources 96,Activities 96,Further Reading 96.
4 Quantum Spookiness 97,4 1 Einstein Podolsky Rosen Paradox 97. 4 2 Schr dinger Cat Paradox 102,Problems 105,Resources 106. Further Reading 106,5 Quantized Energies Particle in a Box 107. 5 1 Spectroscopy 107,5 2 Energy Eigenvalue Equation 110. 5 3 The Wave Function 112,5 4 In nite Square Well 119.
5 5 Finite Square Well 128,5 6 Compare and Contrast 133. 5 6 1 Wave Function Curvature 133,5 6 2 Nodes 135,5 6 3 Barrier Penetration 135. 5 6 4 Inversion Symmetry and Parity 136,5 6 5 Orthonormality 136. 5 6 6 Completeness 137,5 7 Superposition States and Time Dependence 137. 5 8 Modern Application Quantum Wells and Dots 146,5 9 Asymmetric Square Well Sneak Peek at.
Perturbations 147,5 10 Fitting Energy Eigenstates by Eye or by. Computer 150,5 10 1 Qualitative Eyeball Solutions 150. Contents ix,5 10 2 Numerical Solutions 151,5 10 3 General Potential Wells 154. Summary 154,Problems 156,Resources 159,Activities 159. Further Reading 160,6 Unbound States 161,6 1 Free Particle Eigenstates 161.
6 1 1 Energy Eigenstates 161,6 1 2 Momentum Eigenstates 163. 6 2 Wave Packets 168,6 2 1 Discrete Superposition 168. 6 2 2 Continuous Superposition 171,6 3 Uncertainty Principle 176. 6 3 1 Energy Estimation 180,6 4 Unbound States and Scattering 181. 6 5 Tunneling Through Barriers 188,6 6 Atom Interferometry 192.
Summary 197,Problems 197,Resources 201,Activities 201. Further Reading 201,7 Angular Momentum 202,7 1 Separating Center of Mass and Relative. Motion 204,7 2 Energy Eigenvalue Equation in Spherical. Coordinates 208,7 3 Angular Momentum 210,7 3 1 Classical Angular Momentum 210. 7 3 2 Quantum Mechanical Angular,Momentum 210, 7 4 Separation of Variables Spherical Coordinates 215.
7 5 Motion of a Particle on a Ring 218,7 5 1 Azimuthal Solution 220. 7 5 2 Quantum Measurements on a Particle,Con ned to a Ring 223. 7 5 3 Superposition States 224,7 6 Motion on a Sphere 227. 7 6 1 Series Solution of Legendre s Equation 228,7 6 2 Associated Legendre Functions 233. 7 6 3 Energy Eigenvalues of a Rigid Rotor 236,7 6 4 Spherical Harmonics 237.
7 6 5 Visualization of Spherical Harmonics 240,x Contents. Summary 245,Problems 245,Resources 249,Activities 249. 8 Hydrogen Atom 250,8 1 The Radial Eigenvalue Equation 250. 8 2 Solving the Radial Equation 252,8 2 1 Asymptotic Solutions to the Radial. Equation 252,8 2 2 Series Solution to the Radial Equation 253.
8 3 Hydrogen Energies and Spectrum 256,8 4 The Radial Wave Functions 261. 8 5 The Full Hydrogen Wave Functions 263,8 6 Superposition States 270. Summary 272,Problems 272,Resources 274,Activities 274. Further Reading 274,9 Harmonic Oscillator 275,9 1 Classical Harmonic Oscillator 275. 9 2 Quantum Mechanical Harmonic Oscillator 277,9 3 Wave Functions 284.
9 4 Dirac Notation 289,9 5 Matrix Representations 293. 9 6 Momentum Space Wave Function 296,9 7 The Uncertainty Principle 298. 9 8 Time Dependence 300,9 9 Molecular Vibrations 305. Summary 307,Problems 308,Resources 311,Activities 311. Further Reading 311,10 Perturbation Theory 312,10 1 Spin 1 2 Example 313.
10 2 General Two Level Example 317,10 3 Nondegenerate Perturbation Theory 319. 10 3 1 First Order Energy Correction 320,10 3 2 First Order State Vector Correction 324. 10 4 Second Order Nondegenerate Perturbation,Theory 329. 10 5 Degenerate Perturbation Theory 336,10 6 More Examples 343. Contents xi,10 6 1 Harmonic Oscillator 343,10 6 2 Stark Effect in Hydrogen 346.
Summary 351,Problems 352,11 Hyper ne Structure and the Addition of. Angular Momenta 355,11 1 Hyper ne Interaction 355,11 2 Angular Momentum Review 357. 11 3 Angular Momentum Ladder Operators 359, 11 4 Diagonalization of the Hyper ne Perturbation 361. 11 5 The Coupled Basis 365,11 6 Addition of Generalized Angular Momenta 370. 11 7 Angular Momentum in Atoms and Spectroscopic,Notation 377.
Summary 377,Problems 379,Resources 381,Activities 381. Further Reading 381,12 Perturbation of Hydrogen 382. 12 1 Hydrogen Energy Levels 382,12 2 Fine Structure of Hydrogen 386. 12 2 1 Relativistic Correction 386,12 2 2 Spin Orbit Coupling 388. 12 3 Zeeman Effect 393,12 3 1 Zeeman Effect without Spin 394.
12 3 2 Zeeman Effect with Spin 396,12 3 2 1 Weak magnetic eld 396. 12 3 2 2 Strong magnetic eld 402,12 3 2 3 Intermediate magnetic eld 403. 12 3 3 Zeeman Perturbation of the 1s,Hyper ne Structure 405. Summary 407,Problems 407,Resources 409,Activities 409. Further Reading 409,13 Identical Particles 410,13 1 Two Spin 1 2 Particles 410.
13 2 Two Identical Particles in One Dimension 414,13 2 1 Two Particle Ground State 415. 13 2 2 Two Particle Excited State 416,13 2 3 Visualization of States 417. 13 2 4 Exchange Interaction 420,xii Contents,13 2 5 Consequences of the Symmetrization. Postulate 421,13 3 Interacting Particles 423,13 4 Example The Helium Atom 427. 13 4 1 Helium Ground State 428,13 4 2 Helium Excited States 431.
13 5 The Periodic Table 434,13 6 Example The Hydrogen Molecule 437. 13 6 1 The Hydrogen Molecular Ion H 2 438,13 6 2 The Hydrogen Molecule H2 440. Summary 442,Problems 442,Resources 444,Further Reading 444. 14 Time Dependent Perturbation Theory 445,14 1 Transition Probability 445. 14 2 Harmonic Perturbation 450,14 3 Electric Dipole Interaction 454.
14 3 1 Einstein Model Broadband Excitation 456,14 3 2 Laser Excitation 460. 14 4 Selection Rules 462,Summary 466,Problems 467,Resources 468. Further Reading 468,15 Periodic Systems 469,15 1 The Energy Eigenvalues and Eigenstates of a. Periodic Chain of Wells 471,15 1 1 A Two Well Chain 471. 15 1 2 N Well Chain 473,15 2 Boundary Conditions and the Allowed Values.
15 3 The Brillouin Zones 478, 15 4 Multiple Bands from Multiple Atomic Levels 478. 15 5 Bloch s Theorem and the Molecular States 480,15 6 Molecular Wave Functions a Gallery 482. 15 7 The Density of States 484,15 8 Calculation of the Model Parameters 486. 15 8 1 LCAO Summary 488,15 9 The Kronig Penney Model 489. 15 10 Practical Applications Metals Insulators and. Semiconductors 491,15 11 Effective Mass 494,15 12 Direct and Indirect Band Gaps 496.
15 13 New Directions Low Dimensional Carbon 497,Contents xiii. Summary 498,Problems 499,Resources 500,Activities 500. Further Reading 500,16 Modern Applications of Quantum Mechanics 502. 16 1 Manipulating Atoms with Quantum,Mechanical Forces 502. 16 1 1 Magnetic Trapping 502,16 1 2 Laser Cooling 506.
16 2 Quantum Information Processing 514,16 2 1 Quantum Bits Qubits 515. 16 2 2 Quantum Gates 518,16 2 3 Quantum Teleportation 524. Summary 526,Problems 527,Resources 528,Further Reading 528. Appendix A Probability 529,Appendix B Complex Numbers 533. Appendix C Matrices 537,Appendix D Waves and Fourier Analysis 541.
Appendix E Separation of Variables 547,Appendix F Integrals 549. 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

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