Understanding Quantum Physics A User’s Manual

690 Pages·1990·18.972 MB·English

by  Michael A. Morrison

A USER'S MANUAL
Understanding
Quantum Physics
A User's Manual

Understanding
Quantum Physics
A User's Manual
Michael A. Morrison
University ofOklahoma
II
Prentice Hall, Englewood Cliffs, New Jersey 07632
LibraryofCongressCataloging-in-PublicationData
Morrison, Michael A.,(date)
Understandingquantumphysics: auser's manual/byMichael A.
Morrison.
p. cm.
Includes bibliographical references.
Contents: v, I. Fundamentals
ISBN0-13-747908-5(v. I)
I. Quantumtheory. I. Title.
QC174.I2.M69 1990 530.I'2--<1c20 89-48295
CIP
Editorial/productionsupervision: DebraWechsler
Coverdesign: BenSantoni
Manufacturing buyer: PaulaMassenaro
@1990byPrentice-Hall,Inc.
ADivisionofSimon& Schuster
Englewood Cliffs,NewJersey07632
Allrightsreserved. Nopartofthisbookmaybe
reproduced,inanyformorbyanymeans,
without permission inwritingfromthepublisher.
PrintedintheUnited StatesofAmerica
10 9 8 7 6 5 4 3 2 I
ISBN 0-13-747908-5
Prentice-Hall International(UK)Limited,London
Prentice-HallofAustraliaPry, Limited,Sydney
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EditoraPrentice-Hall doBrasil,Ltda.,RiodeJaneiro
Tomy wife,Mary
whomade it possible

Contents
PREFACE xv
PartI What's It All About?: A Qualitative Introduction 1
1 INTRODUCTORY:WHYQUANTUMPHYSICS? 1
1.1 The Classical Point of View 3
1.2 Through the Looking Glass: The Quantum Point of View 6
1.3 Final Thoughts: What's It All About? 12
Annotated Selected Readings 13
Exercises and Problems 14
2 INTO THEMICROWORLD:DUALITYAND THE DOUBLESLIT 18
2.1 Waves versus Particles 20
*2.2 On The Nature of Light 21
*2.3 Understanding Diffraction the Classical Way 26
*2.4 Understanding Interference 28
2.5 Double Trouble 31
2.6 It All Started with de Broglie 36
2.7 The Controversial Concept of Complimentarity 40
vII
2.8 Final Thoughts: A Few Words About Words 42
Annotated Selected Readings 42
Exercises and Problems 44
PartII Starting fromScratch 51
3 FIRST POSTULATES:THESTATEFUNCTION AND ITS
INTERPRETATION 51
3.1 Patterns ofPropagating Possibility: Probability Waves 52
3.2 Systems and States Thereof 57
*3.3 Probabilities: A Review 61
3.4 The Gospel According to Born 68
3.5 How to Normalize a State Function 73
3.6 Great Expectations (and Uncertainties) 79
3.7 Final Thoughts: What the State Function Isn't 85
Annotated Selected Readings 87
Exercises and Problems 89
4 AN ILLUSTRATIVEINTERLUDE: WAVE PACKETSIN ONE
DIMENSION 97
4.1 On the Nature ofthe Free-Particle State Function 99
4.2 Wave Packet Construction for Fun and Profit 106
4.3 The Amplitude Function 111
*4.4 Fourier Analysis (A Mathematical Detour) 116
4.5 An Extended Example: The Gaussian Wave Packet
Unmasked 123
4.6 Uncertainty Regained 128
4.7 (Not Quite) All About Momentum 130
4.8 Final Thoughts: A Wealth ofRepresentations 135
Annotated Selected Readings 137
Exercises and Problems 138
5 OBSERVABLESIN QUANTUM PHYSICS:A PRAGMATISTS
APPROACH 143
5.1 Observables for Macroscopic Systems 145
viii Contents
5.2 The Trouble with Momentum 147
5.3 And Now ForSomething Completely Different: The Momentum
Operator 150
5.4 The Operator Postulate 156
5.5 The Mathematics of Operators: An Introduction 159
5.6 Generalizing Our Expectations (and Uncertainties) 166
5.7 Operators and the Correspondence Principle 169
5.8 Final Thoughts: Operators in Momentum Space 173
Annotated Selected Readings 174
Exercises and Problems 175
6 A QUANTUM EQUATIONOFMOTION: THESCHRODINGER
EQUATIONATLAST 180
6.1 What WeTalk About When WeTalk About Motion 183
6.2 Satisfying Examples 189
6.3 A Personality Profileof the TDSE 193
6.4 Superposition Derived 197
6.5 Is Probability Conserved? 200
*6.6 The Free-Particle Wave Packet Revisited 205
*6.7 The Life and Times of a Gaussian Wave Packet 208
6.8 Probability Fluid and Its Flow 214
6.9 Probability Flow inthe Laboratory 221
6.10 Final Thoughts: Quantum Causality 226
Annotated Selected Readings 228
Exercises and Problems 229
7 SIMPLIFYING MATTERS: THE TIME-INDEPENDENT
SCHRODINGER EQUATION 236
7.1 In Search of Separable Wave Functions 238
7.2 Time and Energy 241
7.3 A Profile of the TISE 243
7.4 A Particle inan Escape-ProofBox 249
7.5 A Closer Look at Stationarity 258
*7.6 Superpositions of Stationary States 263
Contents Ix