Quantum mechanics. Theory and experiment

529 Pages·2012·3.081 MB·English

by  Beck M.

QUANTUM MECHANICS
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QUANTUM MECHANICS
Theory and Experiment
Mark Beck

1
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Library of Congress Cataloging-in-Publication Data
Beck, Mark (Mark K.), 1963–
Quantum mechanics : theory and experiment / Mark Beck.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-19-979812-4 (hardcover : alk. paper)
1. Quantum theory—Textbooks. 2.
Mechanics—Textbooks. I. Title.
QC174.12.B43 2012
530.12—dc23 2011042970
1 3 5 7 9 8 6 4 2
Printed in the United States of America
on acid-free paper
For Annie, Marisol, and Lupe, with love.
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Contents

Table of Symbols xiii
Preface xix
1 • MATHEMATICAL PRELIMINARIES 3
1.1 Probability and Statistics 3
1.2 Linear Algebra 9
1.3 References 17
1.4 Problems 17
2 • CLASSICAL DESCRIPTION OF POLARIZATION 2 1
2.1 Polarization 21
2.2 Birefringence 26
2.3 Modifying the Polarization 29
2.4 Jones Vectors and Jones Matrices 31
2.5 Polarization Interferometer 36
2.6 References 39
2.7 Problems 40
Complement to Chapter 2:
2.A Coherence and Interference 42
3 • QUANTUM STATES 4 7
3.1 State Vectors 47
3.2 Basis States 49
3.3 Other States 51
3.4 Probabilities 53
3.5 Complex Probability Amplitudes 55
3.6 Row and Column Vector Notation 57
3.7 Interference 59
3.8 Problems 62
4 • OPERATORS 65
4.1 Operators 65
4.2 The Adjoint Operator 67
4.3 The Projection Operator 69
4.4 The Matrix Representation of Operators 70
4.5 Changing Bases 75
4.6 Hermitian Operators 79
4.7 References 80
4.8 Problems 81
Complement to Chapter 4:
4.A Similarity Transformations 83
5 • MEASUREMENT 8 9
5.1 Measuring Polarization 89
5.2 The Postulates of Quantum Mechanics 91
5.3 Expectation Values 94
5.4 Operators and Measurements 96
5.5 Commutation and Indeterminacy Relations 97
5.6 Complementarity 101
5.7 References 103
5.8 Problems 103
Complement to Chapter 5
5.A ‘‘Measuring’’ a Quantum State 106
6 • SPIN-1/2 1 11
6.1 The Stern-Gerlach Experiment 111
6.2 Spin States 114
6.3 More Spin States 116
6.4 Commutation Relations 120
6.5 Particle Interference 121
6.6 References 124
6.7 Problems 124
7 • ANGULAR MOMENTUM AND ROTATION 1 27
7.1 Commuting Observables 127
7.2 Angular Momentum Operators 128
7.3 Eigenvalues and Eigenstates 130
7.4 Spin-1 133
7.5 Rotation 134
viii • CONTENTS
7.6 Spin of a Photon 137
7.7 References 138
7.8 Problems 139
Complements to Chapter 7
7.A Compatible Observables 141
7.B Eigenvalues and Eigenstates of Angular Momentum 146
8 • TWO-PARTICLE SYSTEMS AND ENTANGLEMENT 1 53
8.1 Pairs of Photons 153
8.2 Entangled States 159
8.3 Mixed States 163
8.4 Testing Local Realism 165
8.5 References 171
8.6 Problems 171
Complements to Chapter 8:
8.A The Density Operator 175
8.B The Bell-Clauser-Horne Inequality 182
8.C Two Spin-1/2 Particles 188
9 • TIME EVOLUTION AND THE SCHRÖDINGER EQUATION 1 93
9.1 The Time-Evolution Operator 193
9.2 The Schrödinger Equation 194
9.3 Expectation Values 196
9.4 Spin-1/2 Particle in a Magnetic Field 197
9.5 Neutrino Oscillations 200
9.6 References 203
9.7 Problems 203
Complement to Chapter 9:
9.A Magnetic Resonance 206
10 • POSITION AND MOMENTUM 2 15
10.1 Position 215
10.2 Momentum 221
10.3 The Momentum Basis 227
10.4 Problems 231
Complement to Chapter 10:
10.A Useful Mathematics 233
11 • WAVE MECHANICS AND THE SCHRÖDINGER EQUATION 2 41
11.1 The Schrödinger Equation Revisited 241
11.2 Constant Potential–the Free Particle 246
11.3 Potential Step 247
CONTENTS • ix