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