Quantum Concepts in Physics: An Alternative Approach to the Understanding of Quantum Mechanics

462 Pages·2013·14.23 MB·English

by  Malcolm Longair

QuantumConceptsinPhysics
Writtenforadvancedundergraduates,physicists,andhistoriansandphilosophersofphysics,
thisbooktellsthestoryofthedevelopmentofourunderstandingofquantumphenomena
throughtheextraordinaryyearsofthefirstthreedecadesofthetwentiethcentury.
Rather than following the standard axiomatic approach, this book adopts a histori-
cal perspective, explaining clearly and authoritatively how pioneers such as Heisenberg,
Schro¨dinger, Pauli and Dirac developed the fundamentals of quantum mechanics and
merged them into a coherent theory, and why the mathematical infrastructure of quan-
tum mechanics has to be as complex as it is. The author creates a compelling narrative,
providing a remarkable example of how physics and mathematics work in practice. The
bookencouragesanenhancedappreciationoftheinteractionsbetweenmathematics,theory
and experiment, helping the reader gain a deeper understanding of the development and
contentofquantummechanicsthanwithanyothertextatthislevel.
MalcolmLongair is Emeritus Jacksonian Professor of Natural Philosophy and Director of
Development at the Cavendish Laboratory, University of Cambridge. He has held many
highlyrespectedpositionswithinphysicsandastronomy,andhehasservedonandchaired
many international committees, boards and panels, working with both NASA and the
European Space Agency. He has received much recognition for his work, including the
PilkingtonPrizeoftheUniversityofCambridgeforExcellenceinTeachingandaCBEin
themillenniumhonourslistforhisservicestoastronomyandcosmology.Hispreviouswell-
received books for Cambridge University Press include Theoretical Concepts in Physics
(2003),TheCosmicCentury:AHistoryofAstrophysicsandCosmology(2005)andHigh
EnergyAstrophysics(2011).
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Quantum Concepts in Physics
An Alternative Approach to the Understanding
of Quantum Mechanics
MALCOLM LONGAIR
CavendishLaboratory,UniversityofCambridge
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ForDeborah
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Contents
Preface pagexii
Acknowledgements xvi
PartI TheDiscoveryofQuanta
1 Physicsandtheoreticalphysicsin1895 3
1.1 Thetriumphofnineteenthcenturyphysics 3
1.2 Atomsandmoleculesinthenineteenthcentury 4
1.3 ThekinetictheoryofgasesandBoltzmann’sstatisticalmechanics 6
1.4 Maxwell’sequationsfortheelectromagneticfield 11
1.5 TheMichelson–Morleyexperimentandthetheoryofrelativity 13
1.6 Theoriginofspectrallines 15
1.7 Thespectrumofblack-bodyradiation 19
1.8 Thegatheringstorm 23
2 Planckandblack-bodyradiation 24
2.1 Thekeyroleofexperimentaltechnique 24
2.2 1895–1900:Thechanginglandscapeofexperimentalphysics 25
2.3 Planckandthespectrumofblack-bodyradiation 29
2.4 Towardsthespectrumofblack-bodyradiation 36
2.5 Comparisonofthelawsforblack-bodyradiationwithexperiment 41
2.6 Planck’stheoryofblack-bodyradiation 42
2.7 Planckand‘naturalunits’ 45
2.8 Planckandthephysicalsignificanceofh 46
3 Einsteinandquanta1900–1911 48
3.1 Einsteinin1905 48
3.2 EinsteinonBrownianmotion 49
3.3 Onaheuristicviewpointconcerningtheproductionand
transformationoflight(Einstein1905a) 50
3.4 Thequantumtheoryofsolids 55
3.5 Debye’stheoryofspecificheats 58
3.6 Fluctuationsofparticlesandwaves–Einstein(1909) 60
3.7 TheFirstSolvayConference 64
3.8 Theendofthebeginning 67
vii
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viii Contents
PartII TheOldQuantumTheory
4 TheBohrmodelofthehydrogenatom 71
4.1 TheZeemaneffect:LorentzandLarmor’sinterpretations 71
4.2 Theproblemsofbuildingmodelsofatoms 74
4.3 ThomsonandRutherford 75
4.4 Haas’sandNicholson’smodelsofatoms 79
4.5 TheBohrmodelofthehydrogenatom 80
4.6 MoseleyandtheX-rayspectraofthechemicalelements 83
4.7 TheFranck–Hertzexperiment 88
4.8 ThereceptionofBohr’stheoryoftheatom 89
5 SommerfeldandEhrenfest–generalisingtheBohrmodel 90
5.1 Introduction 90
5.2 Sommerfeld’sextensionoftheBohrmodeltoellipticalorbits 91
5.3 Sommerfeldandthefine-structureconstant 96
5.4 Amathematicalinterlude–fromNewtontoHamilton–Jacobi 99
5.5 Sommerfeld’smodeloftheatominthreedimensions 109
5.6 Ehrenfestandtheadiabaticprinciple 113
5.7 Thedevelopinginfrastructureofquantumtheory 118
6 Einsteincoefficients,Bohr’scorrespondenceprincipleandthefirstselectionrules 119
6.1 Theproblemoftransitionsbetweenstationarystates 119
6.2 Onthequantumtheoryofradiation(Einstein1916) 120
6.3 Bohr’scorrespondenceprinciple 123
6.4 Thefirstselectionrules 127
6.5 Thepolarisationofquantisedradiationandselectionrules 129
6.6 TheRydbergseriesandthequantumdefect 132
6.7 Towardsamorecompletequantumtheoryofatoms 135
7 Understandingatomicspectra–additionalquantumnumbers 137
7.1 Opticalspectroscopy,multipletsandthesplittingofspectrallines 137
7.2 TheStarkeffect 138
7.3 TheZeemaneffect 142
7.4 TheanomalousZeemaneffect 145
7.5 TheBarnett,Einstein–deHaasandStern–Gerlachexperiments 151
8 Bohr’smodeloftheperiodictableandtheoriginofspin 155
8.1 Bohr’sfirstmodeloftheperiodictable 155
8.2 TheWolfskehllecturesandBohr’ssecondtheoryoftheperiodictable 157
8.3 X-raylevelsandStoner’srevisedperiodictable 164
8.4 Pauli’sexclusionprinciple 168
8.5 Thespinoftheelectron 169
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ix Contents
9 Thewave–particleduality 172
9.1 TheComptoneffect 172
9.2 Bose–Einsteinstatistics 174
9.3 DeBrogliewaves 177
9.4 Electrondiffraction 181
9.5 Whathadbeenachievedbytheendof1924 183
PartIII TheDiscoveryofQuantumMechanics
10 Thecollapseoftheoldquantumtheoryandtheseedsofitsregeneration 189
10.1 Ladenburg,Kramersandthetheoryofdispersion 189
10.2 SlaterandtheBohr–Kramers–Slatertheory 194
10.3 Bornand‘quantummechanics’ 197
10.4 MathematicsandphysicsinGo¨ttingen 200
11 TheHeisenbergbreakthrough 203
11.1 HeisenberginGo¨ttingen,CopenhagenandHelgoland 203
11.2 Quantum-theoreticalre-interpretationofkinematicandmechanical
relations(Heisenberg,1925) 205
11.3 Theradiationproblemandthetranslationfromclassical
toquantumphysics 207
11.4 Thenewdynamics 212
11.5 Thenonlinearoscillator 214
11.6 Thesimplerotator 221
11.7 Reflections 222
12 Matrixmechanics 224
12.1 Born’sreaction 224
12.2 BornandJordan’smatrixmechanics 226
12.3 Born,HeisenbergandJordan(1926)–theThree-ManPaper 232
12.4 Pauli’stheoryofthehydrogenatom 241
12.5 Thetriumphofmatrixmechanicsanditsincompleteness 245
13 Dirac’squantummechanics 247
13.1 Dirac’sapproachtoquantummechanics 247
13.2 DiracandThefundamentalequationsofquantummechanics(1925) 248
13.3 Quantumalgebra,q-andc-numbersandthehydrogenatom 255
13.4 Multi-electronatoms,OnquantumalgebraandaPhDdissertation 259
14 Schro¨dingerandwavemechanics 261
14.1 Schro¨dinger’sbackgroundinphysicsandmathematics 261
14.2 Einstein,DeBroglieandSchro¨dinger 263
14.3 TherelativisticSchro¨dingerwaveequation 267
14.4 QuantisationasanEigenvalueProblem(Part1) 269
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