Basic Concepts of Quantum Mechanics

267 Pages·2021·4.463 MB·English

by  Lev Vasilʹevich Tarasov

Although quantum mechanics
L. V. Tarasov Basic
deals with microparticles, its
significance is by no means
Concepts limited to microphenomena.
In our endless quest for
understanding and perfecting
of
our knowledge of the laws of
nature, quantum mechanics
represents an important
qualitative leap.
antum
Mechanics
MIR Publishers Moscow

L. TARASO V
B A S I C C O N C E P T S O F
Q U A N T U M M E C H A N I C S
L.V. Tarasov
Basic Concepts of Quantum Mechanics
TranslatedfromtheRussianbyRamS.Wadhwa
TypesetinLATEX byDamitrMazanov
Mir Publishers Moscow
Firstpublished1980.
Revisedfromthe1978Russianedition1979
Englishtranslation,MirPublishers,1980
Thiselectronicversionreleasedonthewebbyhttp://mirtitles.orgin2021.
GITProjectpageforsourcefileshttps://gitlab.com/mirtitles/tarasov-qm

Contents
Preface 9
Prelude: Can the System of Classical Physics Concepts Be Considered Logically
Perfect? 15
1 Physics of the Microparticles 21
1 CertainCharacteristicsandPropertiesofMicroparticles 23
2 TwoFundamentalIdeasofQuantumMechanics 29
3 UncertaintyRelations 38
4 SomeResultsEnsuingfromtheUncertaintyRelations 45
5 ImpossibilityofClassicalRepresentationofaMicroparticle 51
6 RejectionofIdeasofClassicalPhysics 56
Interlude: Isa“PhysicallyIntuitive”ModelofaMicroparticlePossible? 63
2 Physical Foundations of Quantum Mechanics 67
7 SomeBasicExperiments 69
8 AmplitudesofTransitionProbabilities(FormulationofBasicPrinciples) 78
6
9 AmplitudesofTransitionProbabilities(DemonstrationofBasicPrinciples) 83
10 SuperpositionofStates 95
11 MeasurementinQuantumMechanics 104
Interlude: AreThesetheSameWaves?,Or,AgainonWavesinQuantumMechanics
112
12 CausalityinQuantumMechanics 115
13 MicroparticleswithTwoBasicStates 120
14 TheElectroninaMagneticField 129
15 TheWaveFunction 135
16 QuantumMechanicsasaQualitativeLeapinMan’sKnowledgeoftheLawsof Nature
139
ABriefInterlude 147
Interlude: DoQuantum-MechanicalConceptsContradictOurCommonSense? 153
3 Linear Operators in Quantum Mechanics 159
17 ABriefLookattheTheoryofLinearOperators 162
18 FromHamiltonianMatrixtoEnergyOperator 170
19 LinearOperatorsinQuantumMechanics 176
20 TheQuantum-MechanicalApparatusinCoordinateRepresentation 182
21 ApplicationsoftheSchrödingerEquation 192
22 TheHamiltonianinSomeSpecificProblems 204
23 TransitiontotheMomentumRepresentation 210
24 AnElectroninaPeriodicField 215
7
25 TheProbabilityofQuantumTransitions 222
26 WaysofDescribingEvolutionofMicrosystemswithTime 227
A Brief Historical Survey 233
Appendices 243
A EigenvaluesandEigenfunctionsofaHermitianOperator 244
B TransitionfromQuantumMechanicstoClassicalMechanics 245
C CommutationRelations 246
D CommutationofOperators𝑀ˆ2,𝑀ˆ𝑖 248
E SomeSpecialFunctions 249
F LinearHarmonicOscillator 252
Subject Index 255
Bibliography 259