www.wiley-vch.de A F Moses Fayngold, Vadim Fayngold longside a thorough definition of basic concepts and their a interrelations, backed by numerous examples, this textbook y n features a rare discussion of quantum mechanics and informa- g tion theory combined in one text. It deals with important topics o hardly found in regular textbooks, including the Robertson- l Quantum Mechanics d Schrödinger relation, incompatibility between angle and angular • momentum, “dispersed indeterminacy”, interaction-free mea- F surements, “submissive quantum mechanics”, and many a Moses Fayngold graduated from the others. With its in-depth discussion of key concepts complete y and Quantum State University of Samarkand and with problems and exercises, this book is poised to become n got his PhD at the Nuclear Research the standard textbook for advanced undergraduate and begin- g Institute of Academy of Science in o ning graduate quantum mechanics courses and an essential Uzbekistan (former USSR). He has ld reference for physics students and physics professionals. combined teaching and research in Information colleges of USSR and USA, most recently as a Senior University Lectur- er at the Physics Department of the From the contents: New Jersey Institute of Technology. He has lectured on Quantum Mech- • Embryonic Quantum Mechanics: Basic Features anics and Special Relativity to both • Playing with the Amplitudes undergraduate and graduate students. • Representations and the Hilbert Space His research interests and areas of activity include Special and General • Angular Momentum Relativity, Quantum Mechanics, • Evolution of Quantum States Optics and optical imaging, particle • Indeterminacy Revisited scattering and propagation in peri- • “Submissive” Quantum Mechanics odic structures. • Quantum Statistics aQ n • Second Quantization u d • Quantum Mechanics and Measurements a • Quantum Non-Locality Qn t • Quantum Measurements and POVMs uu • Quantum Information am n • Quantum Gates t M • Quantum Key Distribution u me c Vadim Fayngold holds two degrees – Ih n M.S. in Physics and B.S. in Computer a Science. While working as a research fon assistant at the Department of Com- ric m puter Engineering (Polytechnic Uni- s versity, New York), he focused on a computer simulation of complex t i processes in fluid dynamics. The o combined expertise he developed n there has spurred his interest in the Quantum Information theory. Vadim came to the idea of writing this book while working on computer animations of various relativistic and ISBN 978-3-527-40647-0 quantum-mechanical phenomena. PHYSICS TEXTBOOK MosesFayngoldandVadim Fayngold QuantumMechanicsand QuantumInformation RelatedTitles Furusawa,A.,vanLoock,P. Hameka,H.F. QuantumTeleportationand QuantumMechanics Entanglement AConceptualApproach AHybridApproachtoOpticalQuantum 2004 InformationProcessing Softcover ISBN:978-0-471-64965-6 2011 Hardcover Phillips,A.C. ISBN:978-3-527-40930-3 IntroductiontoQuantum Gazeau,J.-P. Mechanics CoherentStatesinQuantum 2003 Physics Softcover ISBN:978-0-470-85324-5 2009 Hardcover Zettili,N. ISBN:978-3-527-40709-5 QuantumMechanics Bruß,D.,Leuchs,G.(eds.) ConceptsandApplications LecturesonQuantum 2001 Information Softcover ISBN:978-0-471-48944-3 2007 Softcover Merzbacher,E. ISBN:978-3-527-40527-5 QuantumMechanics Audretsch,J.(ed.) 1998 EntangledWorld Softcover ISBN:978-0-471-88702-7 TheFascinationofQuantumInformation andComputation Cohen-Tannoudji,C.,Diu,B.,Laloe,F. 2006 QuantumMechanics Hardcover ISBN:978-3-527-40470-4 2VolumeSet 1977 Stolze,J.,Suter,D. Softcover QuantumComputing ISBN:978-0-471-56952-7 AShortCoursefromTheoryto Experiment 2004 Softcover ISBN:978-3-527-40438-4 Moses Fayngold and Vadim Fayngold Quantum Mechanics and Quantum Information AGuidethroughtheQuantumWorld The Authors All books published by Wiley-VCH are carefully produced . Neverthel ess, authors, editors, and publisher do not warrant the information contained Moses Fayngold in these books, inclu ding this book, to be free of NJIT errors. Rea ders are advised to keep in mind that Dept. of Physi cs statemen ts, data, illust rations, procedural details or Newark, NJ 07102-1982 other items may inadver tently be inaccurate . fayngold@mai laps.org Library of Congress Car d No.: applied for Vadim Fayngold British Library Catalogu ing-in-Publica tion Dat a vadim.resear [email protected] A catalogu e record for this book is av ailable from the British Library. Bibliog raphic inform ation publ ished by the Deutsche Nation albibliothek The D eutsche Na tionalbibliothe k lists this publicatio n in the Deutsche Nationalbibli ografi e; detailedbibliographicdataareavailableonthe Internet at < http:// dnb.d-nb.d e> . #2013Wiley-VCHVerlagGmbH&Co.KGaA, Boschstr.12,69469Weinheim,Germany Allrightsreserved(includingthoseoftranslationinto otherlanguages).Nopartofthisbookmaybe reproducedinanyform–byphotoprinting, microfilm,oranyothermeans–nortransmittedor translatedintoamachinelanguagewithoutwritten permissionfromthepublishers.Registerednames, trademarks,etc.usedinthisbook,evenwhennot specificallymarkedassuch,arenottobeconsidered unprotectedbylaw. PrintISBN: 978-3-527-40647-0 CoverDesign AdamDesign,Weinheim,Germany Typesetting ThomsonDigital,Noida,India PrintingandBinding MarkonoPrintMediaPteLtd, Singapore j V Contents Preface XIII AbbreviationsandNotations XIX 1 TheFailureofClassicalPhysics 1 1.1 BlackbodyRadiation 1 1.2 HeatCapacity 4 1.3 ThePhotoelectricEffect 9 1.4 AtomsandTheirSpectra 12 1.5 TheDouble-SlitExperiment 14 Problem 19 References 19 2 TheFirstStepsintotheUnknown 21 2.1 TheBBRandPlanck’sFormula 21 2.2 Einstein’sLightQuantaandBBR 24 2.2.1 Discussion 27 2.3 PEERevisited 30 2.4 TheThirdBreakthrough:deBroglieWaves 31 2.4.1 Exercise 33 Problems 35 References 35 3 EmbryonicQuantumMechanics:BasicFeatures 37 3.1 AGlimpseoftheNewRealm 37 3.2 Quantum-MechanicalSuperpositionofStates 39 3.3 WhatIsWavingThere(theMeaningoftheC-Function)? 42 3.4 ObservablesandTheirOperators 47 3.5 Quantum-MechanicalIndeterminacy 49 3.6 IndeterminacyandtheWorld 53 3.7 QuantumEntanglementandNonlocality 58 3.8 Quantum-MechanicalPhaseSpace 62 3.9 DeterminismandCausalityinQuantumWorld 63 j VI Contents 3.9.1 Discussion 63 Problems 66 References 66 4 PlayingwiththeAmplitudes 69 4.1 CompositionofAmplitudes 69 4.2 DoubleSlitRevisedI 74 4.3 DoubleSlitRevisedII 77 4.4 NeutronScatteringinCrystals 78 4.5 BosonicandFermionicStates 81 4.6 PathIntegrals 89 Problems 93 References 93 5 BasicFeaturesandMathematicalStructureofQM 95 5.1 Observables:theDomainofClassicalandQuantum Mechanics 95 5.2 Quantum-MechanicalOperators 97 5.3 AlgebraofOperators 100 5.4 EigenvaluesandEigenstates 102 5.5 OrthogonalityofEigenstates 107 5.6 TheRobertson–Schr€odingerRelation 110 5.7 TheWaveFunctionandMeasurements(Discussion) 112 Problems 116 References 117 6 RepresentationsandtheHilbertSpace 119 6.1 VariousFacesofaStateFunction 119 6.2 UnitaryTransformations 121 6.3 OperatorsintheMatrixForm 125 6.4 TheHilbertSpace 129 6.5 OperationsintheHilbertSpace 135 6.6 NonorthogonalStates 142 Problems 147 References 148 7 AngularMomentum 149 7.1 OrbitalandSpinAngularMomenta 149 7.2 TheEigenstatesandEigenvaluesofL^ 151 7.3 OperatorL^andItsCommutationProperties 154 7.4 SpinasanIntrinsicAngularMomentum 164 7.5 AngularMomentumofaCompoundSystem 183 7.6 SphericalHarmonics 188 Problems 196 References 197 j Contents VII 8 TheSchro€dingerEquation 199 8.1 TheSchr€odingerEquation 199 8.2 StateFunctionandtheContinuityEquation 200 8.3 SeparationofTemporalandSpatialVariables:Stationary States 203 8.4 TheHelmholtzEquationandDispersionEquationforaFree Particle 205 8.5 SeparationofSpatialVariablesandtheRadialSchr€odinger Equation 207 8.6 SuperpositionofDegenerateStates 209 8.7 PhaseVelocityandGroupVelocity 212 8.8 deBroglie’sWavesRevised 218 8.9 TheSchr€odingerEquationinanArbitraryBasis 222 Problems 226 References 226 9 ApplicationstoSimpleSystems:OneDimension 227 9.1 AQuasi-FreeParticle 227 9.2 PotentialThreshold 232 9.3 TunnelingthroughaPotentialBarrier 236 9.4 ColdEmission 241 9.5 PotentialWell 244 9.6 QuantumOscillator 249 9.7 OscillatorintheE-Representation 254 9.8 TheOriginofEnergyBands 257 9.9 PeriodicStructures 260 Problems 269 References 271 10 Three-DimensionalSystems 273 10.1 AParticleina3DBox 273 10.2 AFreeParticlein3D(SphericalCoordinates) 274 10.2.1 Discussion 277 10.3 SomePropertiesofSolutionsinSphericallySymmetric Potential 277 10.4 SphericalPotentialWell 278 10.5 StatesintheCoulombFieldandaHydrogenAtom 281 10.6 AtomicCurrents 287 10.7 PeriodicTable 290 Problems 293 References 294 11 EvolutionofQuantumStates 295 11.1 TheTimeEvolutionOperator 295 11.2 EvolutionofOperators 299 j VIII Contents 11.3 SpreadingofaGaussianPacket 301 11.4 TheB-FactorandEvolutionofanArbitraryState 303 11.5 TheFraudulentLifeofan“Illegal”Spike 306 11.6 JinneeOutoftheBox 311 11.7 InadequacyofNonrelativisticApproximationinDescription ofEvolvingDiscontinuousStates 315 11.7.1 Discussion 316 11.8 Quasi-StationaryStates 317 11.8.1 Discussion 323 11.9 3DBarrierandQuasi-StationaryStates 324 11.10 TheTheoryofParticleDecay 327 11.11 Particle–AntiparticleOscillations 331 11.11.1 Discussion 337 11.12 AWatchedPotNeverBoils(QuantumZenoEffect) 339 11.13 AWatchedPotBoilsFaster 344 Problems 350 References 352 12 QuantumEnsembles 355 12.1 PureEnsembles 355 12.2 Mixtures 356 12.3 TheDensityOperator 358 12.4 TimeEvolutionoftheDensityOperator 366 12.5 CompositeSystems 368 Problems 376 References 376 13 IndeterminacyRevisited 377 13.1 IndeterminacyUnderScrutiny 377 13.2 TheHeisenbergInequalityRevised 380 13.3 TheIndeterminacyofAngularMomentum 382 13.4 TheRobertson–Schr€odingerRelationRevised 384 13.5 TheN–fIndeterminacy 388 13.6 DispersedIndeterminacy 390 Problems 394 References 395 14 QuantumMechanicsandClassicalMechanics 397 14.1 RelationshipbetweenQuantumandClassicalMechanics 397 14.2 QMandOptics 400 14.3 TheQuasi-ClassicalStateFunction 401 14.4 TheWKBApproximation 404 14.5 TheBohr–SommerfeldQuantizationRules 406 Problems 409 References 410