ROOMRAIDERSQuantumTheory：房间攻略的量子理论.ppt

ONTHEROADAGAIN FinalDestination QuantumMechanics TakingtheTripFromClassicalPhysicstoQuantumMechanics WhatisQuantumMechanicsonemayask Well inanutshell quantummechanicsis TheFUNdamentalbranchofphysicsreplacingclassicalNewtonianMechanicsandElectromagnetismattheatomicandsubatomiclevels QuantummechanicsprovidesexplanationsformanyphenomenathatareunattainablethroughclassicalmechanicsNamely quantization wave particleduality theuncertaintyprinciple quantumentanglement Don tbefooled thiswillbenoshorttrip Quantumtheoryideasdidnotoriginateovernight Therewerenumerousexperimentsandobservedphenomenathateventuallyledtothismodernwayofthought ThemovefromGeneralRelativitytoQuantummechanicsisahugestep sincethetwotheoriesseeminglycontradicteachother Thetwofundamentalissuesyieldingthiscontradictionare ClassicalisessentiallyadeterministicapproachwhilequantummechanicsisessentiallyindeterministicGeneralrelativityreliesmainlyongravitywhilequantummechanicsreliesonthreefundamentalforces thestrong weak andelectromagnetic thoughtheseforcesareimperativeinQuantumTheory wewillleaveoutadiscussionofthemhere fortheywillbecoveredinalatterpresentation Fortheremainder Wewilllookatthemajorplayersontheroadtothediscoveryanddevelopmentofthiswayofthought Whyarewegoinghere Twofundamentaldiscrepanciesbetweenexperimentalobservationsandclassicalphysicswerenoticedinthelate1800 s Thesetwodiscrepancies namely theultravioletcatastropheandthediscretespectrallinephenomena causedscientisttore examineseveralestablishedideasandarriveatanewwayofthought EVERYONEJUMPINTHEVAN We rehittintheroad Problem1 EnergyandBlackbodyradiationIntro AblackbodyisasurfacewhichabsorbsallradiationandatagiventemperatureT canalsoemitradiationThus usingthe T energyfunction holdingTconstant theindividualwavelengths oftheradiationcanbeanalyzedAttheturnofthe20thcentury thisinfactwasdoneandtheobservationswerefirstrecordedbyOttoLummerandErnstPringsheimandthenagainthefollowingyearbyHeinrichRubensandFerdinandKurlbaumTheresultsgatheredareshowninthefollowingfigure Results UhOh AccordingtotheEquipartitionTheorem anon quantumtheorem everydegreeoffreedomofasystemmustshareequallyintheenergyavailabletothesystem Takeforexample ablackbodyradiationofdimensionl thenweknowthatwavelengthsaregivenby 2l n wheren 1 2 3 Eachoftheserepresentadegreeoffreedom andtherefore bytheequipartitiontheorem shouldsharetheenergyequally Thus sincethereareinfinitelymanywavesasthewavelengthgetsshorter itwouldbeassumedthatthemajorityofthelight ieradiation wouldbeattheshortwavelengthendofthespectrum asshownbythedottedline Noticethedottedline Whyisthisaproblem Letsdothemath Amajorproblemarises sinceweknowfromderivationsthatfollowdirectlyfromtheequipartitiontheorem donebyRayleighandSirJamesJeans thatthroughclassicalanalysis theenergydensityfunctioncanbeexpressedas wherekisBoltzmann sconstantButitiseasilyseenthatbyapplyingbasiccalculusthelimitofas approaches0 isinfinity Obviouslycontradictingtheobservedresultsshowninthefigurebythesolidline Ifthiswereindeedthecase theresultswouldbedescribedbythedottedlineinthepreviousfigure Thisdiscrepancyand blow up atshortwavelengthsisoftenreferredtoasthe ultra violetcatastrophe andspurredmuchthoughtastohowtoremedyit FLATTIRE Ourclassiccarisgettingold timetotradeitin Thediscrepancybetweentheobservationalresultsandthisequationisanintenseproblem SincetheenergydensityequationderivedbyJeansin1905 followeddirectlyfromthewellestablishedequipartitiontheorem whichwasaconsequenceofgeneralrelatively Thusbecausethesedonotcorrelate itimpliesthattheoverlyingtheorymustbeinadequate Problem1 FlatTirenowwehaveProblem2 runningoutofgas ThesecondphenomenaleadingtoquantumtheorystemsfromthepatternofspectrallinesemittedbyanelementWhenanelectricarcpassesthroughasampleofgas itisobservedthatonlycertainfrequenciesoflightarepresent Whenobservingthespectrallinesbyseparatingthemwithaprism itisobservedthatthewavelengthsaredistincttotheelementemittingthespectrum What ssobadaboutthat ThisobservationdirectlycontradictsthepredictionsofclassicalphysicsAccordingtoclassicalphysics acceleratedparticlesmustemitelectromagneticradiation andthusiftheyweremovingrandomlywithintheatom allthespectrawouldbeemitted thusproducingacontinuousspectrum howevertheresultsshowedadiscretedistribution Duetothisphenomena scientistbeganassociatingthesespectralemissionwithstableorbits andanempiricalformulawasevendiscoveredthroughtrialanderrorefforts tofittheobservedreality Thisequationis v R 1 m 2 1 n 2 knownasBalmer sEq wherevisthevelocityoffrequenciesofthelines Risauniversalconstant misaconstantrepresentingaparticularseries andnisanintegerrepresentingaparticularline Whatarewegoingtodo Manymodelsoftheatomwhereconstructedtotrytodescribethisphenomena However theynearlyallassumedauniformdistributionofthepositivecharge However in1909 HansGreigerandErnstMarsdendisprovedthistheorythroughcarefulexaminationofthescatteringofabeamofchargedparticles Whatwouldbeexpectedifthepreviousmodelswereinfactreality wouldhavebeenauniformscatteringoftheparticles Howeverthiswasnotthecase Whathappened GriegerandMarsdenusedanexperimentsuggestedbyErnstRutherford apremierphysicistandoftenconsideredtheFaradayofnuclearphysics Theexperimentconsistedofusinggoldtinfoilabout400atomsthickwithHe particlesastheirbombardingprojectiles Mostoftheparticleswentstraightthroughwithnodeflection whichseemedtosupportclassicaltheory sinceitisknownthatelectronsaremuchsmallerandthuswhenallchargeisequallydistributed therewouldbelittledeflectionHOWEVER thiswasnotthecaseforallparticle therewereagivennumberthatwerescatteredbackatangleslargerthan90degrees implyingsomethingelseisgoingon Rutherford examinedtheresultsandconcludedthatthebulkoftheatomandthemajorityofpositivecharge HADtobeconcentratedatasinglepointintheatom Thus theconceptofanuclearatommodelwaspresented However thiscausesmoreproblems Withthismodel underclassicaltheory itwouldnecessarilyyieldacontinuousspectrum sincethereisnopartitioningoftheenergy thusnoconstraintsoneitherthefrequencyorwavelength Withclassicaltheoryagainfailingtoexplaintheobservedphenomena physicistbegansearchingforanexplanationandtheorythataccuratelydescribesreality Nowthatweknowtheproblems letfixthem Letsmeetthemechanics TheBigWigs MaxPlank NielsBohr AlbertEinstein deBroglieOthernotableparticipants MaxBorn JohnvonNeumann PaulDirac WhoisMaxPlank BriefBackground Planckcamefromtraditionallyintellectualbackground hisgreatgrandfatherandgrandfatherwereboththeologyprofessors whilehisfatherwasalawprofessorandunclewasajudgeHestudiedunderHermannMulleratMunich sK niglichesMaximiliangymnasium wherehewastaughtmechanics astronomy andmathematicsAnincrediblygiftedchild hegraduatedattheageof16andin1874beganstudyingatuniversityofMunich BackgroundContinued Whileatuniversity hewasadvisedbyhisprofessorsnottostudyphysics becausetheybelievedthatnearlyeverythinghadalreadybeendiscoveredandallthatwaslefttodowasfillinafewholesHowever thisdidnotdiscouragePlanck ratherheclaimedthathewasnotinthefieldtomakerevolutionarydiscoveries butrathertogainafullerunderstandingofthosetheoriesalreadyestablishedThisdesireforcompleteunderstanding consequentlyledhimtoarguably oneofthegreatestdiscoveriesinmodernphysics sinceherefusedtoacceptthatclassicaltheoryjustdidn texplainreality Careerbackground Planckdidveryfewexperimentsbeforeenteringintotherealmoftheoreticalphysics Hewasmoreconcernedwithwhythingswerehappening thansearchingfornewobservationalrealitiesHewenttoBerlintostudywithtwoofthepremierephysicistsofthetime HermannvonHelmholtzandKirchhoffStudyingentropyandthermodynamics hewaseventuallyappointedtothepositionofKirchhoff ssuccessorTheseeventsgavehimthebackgroundneededtomakehisrevolutionarydiscoveries WhatexactlywerePlanck sfindings PlanckworkedontheBlackbodyradiationproblemPlankwashiredbyelectricalcompaniestofindawaytoproducethemostlight radiation usingtheleastamountofenergypossible SincehehadworkedunderKirchhoff PlancknewthatKirchhoffhadalreadycontemplatedthequestionofhowtheintensityoftheradiationemittedbyablackbodydependsonthefrequencyoftheradiationThus Planckdecidedtoutilizeacollectionofradiatingharmonicoscillatorsinthermalequilibriumtodescribeblackbodyradiation QuickReview WeknowthatclassicalmethodshadfailedtodescribetheobservationalrealityasseenthroughitsdiscrepancywiththeRyleigh Jeanequation sinceitfailedtoworkforshortwavelengths TherewasalsoconjecturepresentedbyWillheimWeilthatdescribedthephenomenaforshortwavelengths butfailedforlongwavelengths ThusPlanckdecidedtoutilizebothideasandinterpolatebetweenthetwo Todothis Planckusedathermodynamicalargumenttoproduceatwoparameteradhocexpressionwhichwewillseelater HedidthisthroughmodificationofclassicalrelationsinvolvingentropyofradiationHisargumentwasincrediblycomplex andtoointensetoderivecurrently however itisimperativetonotethatitwasincrediblybasedonphenomologicalcurvefittingBasically hewasleftwithacurvethatfittheobserveddataperfectly buthadnosolidtheoreticaljustificationforhisresults WhyWhyWhy Thus hereturnedtohisstudiesinordertotrytoderiveatheoreticaljustificationTodothis hefoundthathewasrequiredtoutilizestatistical mechanicaltechniques whichallowsfordistributionstobedescribeonitsmicro state whichhadbeenintroducedbyBoltzmann Thiswasabigstep becausehehadbeenextremelyreluctanttoacceptthesenewtechniques becausehefelttheyweremerelyaxiomaticbynatureHowever heclaimed itwasanactofdespair Iwasreadytosacrificeanyofmypreviousconvictionsaboutphysics Thoughhewasoriginallyreluctant heallowedhimselftoacceptthesenewtechniques whichallowedhimtopartitionthetotalenergyofthesystemintodiscreteamountsTherefore hisoscillatorscouldonlyabsorbandemitdiscreteamountsofradiation whichconsequentlyyieldedtheproperdistribution Throughthesemethods hearrivedatthenotionthattheenergyabsorptionandemissionmustbequantizedintodiscreteamounts modernlyreferredtoasquanta Finalresult Thus Planckhadatheoreticalbasisandthereforeshowedthattheenergy isrelatedtothefrequencyvby hv wherehisPlanck sconstant StillHesitant Thoughhewascertainthatenergyabsorptionandemissionhadtobequantized andwasdescribedbytheformula hewasstillhesitanttoacceptenergyquantizationinelectromagneticradiation HefeltthatMaxwell selectrodynamics whichclaimedthatanelectromagneticfieldcouldcarrycontinuouslyvaryingamountsofenergy hadbeentoosuccessfultojustdisregardthemHespentmuchtimetryingtofithispriorfindingof hv intoclassicalelectrodynamics however aftermanyfailedattempts hecametoafinalconclusionacceptingtherealityofquanta whichhassincebeenacceptedbynearlyallphysicists Thisisevidenttoday aswereadilyusethenotionofaphoton whichismerelythenameforaquantizedelectromagneticfield SoWhat Howdoesthissolvetheproblemwhicharisesfromclassicalmechanics Lookattheequationforwavelengthv c weseethatPlancksequation hv hc Thus ifenergyisfinite theremustexistashortestandalongestwavelength andthus ifveryfewquantaarereleasedwhen iseitherlargeorsmall Further itisobviousfromtheequationthatthepeakwilloccuratthemostprobablefrequency MileMarker1 WithPlanck srecognitionthatenergycouldinfactbediscretelyquantized anentirenewwaveofphysicalthoughtarosePlanck sfindingsareoftenconsideredthebirthofquantummechanics However thisismerelythefirststep letsnowlooktotheproblemofdiscreteemissionofspectrallines ANATOMICTRANSMISSION uhtransition NielsBohr WhoisNielsBohr Bohrmademanynotablecontributionstophysics namely AmodeloftheatomicstructureElectronorbitalmomentumisquantizedbyL n NotionthatelectronstravelindiscreteorbitalsNotionthatwhenelectronsdropfromhighertolowerenergy itemitsaphotonTheprincipleofcomplementarity Whyweneedhim Thoughhemadenotablecontributions wewillfocusonhistheoryofatomictransitionsBohrattendedtheUniversityofCopenhagenandthenwenttoManchestertoworkunderRutherford who aswesawpreviously wasactivelyworkingondevelopinganatomicmodelThisinfluencedBohrgreatly andwithinfourmonthsofworkingwithRutherford heformulatedhistheory LetsDerivetheTheory BohrbeganbyassumingRutherford smodel ieanelectronofcharge eandmassmincircularorbitofradiusraboutthenucleus charge e Thus ifastablenuclearorbitistobeattained theelectrostaticforceofattractionmustyieldtheimperativecentripetalforce Whereisthisgoing Knowingthis andapplyingthelawofconservationofenergy Bohrderivedthefollowingexpression whichrepresentsthefrequencyinrelationtoitsenergy However ifweweretoapplyclassicaltheory whichimpliesthatanacceleratedparticleemitsradiationwitfrequencyequaltothatasseenabove problemsobviouslyarise What sWrong Accordingtoclassicaltheory theenergyEcouldbeofanyvalueandthustheatomshouldradiateallfrequencies yieldingacontinuousspectrum However weknowthisisnotthecaseasseenpriorTherefore Bohrbeganworkingtoattainasetofdiscreteorbitssuchthatitisstableonlywhentheelectroniswithinonethethesedistinctorbitals andthusonlyemitsradiationwhentransitioningbetweenthem FollowtheLeader KnowingthatPlanckhadquantizedenergyemittedandabsorbedinoscillators Bohrdecidedtoquantizetheenergyofthephotonsreleasedwhenenteringandleavingthestableorbits Withthisconcept hederivedtheequation Heintroducesthefactorof becauseifthetheelectronisinitiallyatrestanditsfinalstateisinthestableorbit thenitwillhavevelocityv thustheaveragebetweenthetwoissimplyv 2 However itmustbenotedthathedidnotcomeupwiththisjustificationuntilheexaminedBalmer sequation presentedearlier andfoundthatitwasthe factorthatallowedforanaccuratefit Therefore hefeltthattheemittedradiationwouldbesomemultipleofthis whichledtothen 2factor Bycombiningthisderivationwiththeexpressionoffrequencyintermsofenergy BohrobtainedtheexpressionFurther whencombinedwiththeconservationofenergylawE final E initial hv Balmer sequationisobtained andthus thespectrallinesemittedbyHydrogenareaccuratelydepictedbyBohr sexpression EvenBetter Bohralsostatedthatusingthesametechniquesandtheory hisderivedexpression wasequivalenttoquantizingangularmomentuml mvr Thisisveryefficient butsimilartopastexplanations thuswewillnotderivehere DoesitWork Bohr smodelworksquantitativelyforone electronatomssuchashydrogen ionizedhelium anddoublyionizedLithium Thoughhisoriginalmodelonlyworkedforthesefewelements hisworkmadeimmediateimpactandcommandedmuchattention Afterhepresentedhisworkin1913 manygeneralizationsweremadeandasetofrulesfortreatingatomswasestablishes modernlyreferredtoas oldquantumtheory Howwegofromonetoanother Athreestepprocesswasemployedtomovefromclassicaltoquantumtheorywhendescribingatomicstructure Initially classicaltheoryisusedtodeterminethepossiblemotionsofthesystemSecondly quantumtheoryisemployedtodepictthepossibleorbitsAndfinally thelawofenergyconservationisemployedtofixthefrequenciesduringanatomictransition WhoCares DoesitreallymatterhowBohrarrivedathismodeloftheatom orhowBohrdeterminedthatthefrequencyofanatomdependsonthenegativeofitsenergyraisedtothe3 2power DoesanyoneneedtoknowthisbesidesscientifichistoriansandPHIL PHYS30389students ProbablynotHowever insightintotheprocesshelpsmakethediscoveriesmoreunderstandable BrillianceorBackpedaling WeseePlankmakesanadhocattempttomakesomeargumenttojustifyhiscurvefittingThen againsthiswill heacceptsthehypothesisofquantizationEnergyquantizationprovidingthenecessarylimitationontheblackbodyradiationcurveatshortwavelengthswasnotamomentofbrilliancebutinsteadadrawnoutprocessPlankhimselfwantedtoavoid BrillianceorBackpedaling2 Bohrinadesperatepanictoobtainafittothedata ourgoodfriendtheBalmerformula By1913PlanksquantizationofenergyishighlyacceptedsoBohrisnotasadamantaboutavoidingitBohrisconservativeinhismethods forexamplesoughttoquantizeenergyandnotangularmomentumHisattemptstoavoidnumerousnewprinciplesleadstotheacceptanceofhistheoryDon tyouappreciatetheirworkbetternow ForkintheRoad AtthispointinhistorythetheoryofindeterminismwasaseriousquestionfortheenlightenedPoincare H ffding andKierkegaardallincorporatedquantumtheoryintotheirworkH ffdingclaimedthatdecisiveeventsinlifeproceedthroughdiscontinuities orsudden jerks whichfaintlyresemblesatomicphenomenaTheseideaswereinthemindsofscientists whichhelpsexplainwhysomeweremoreinclinedtoacceptcertainmodelsofquantumtheory Team NewSchool turnleft Bohr Heisenberg Pauli Jordon andBornAllfoundinCopenhagenExclusivegroupwhoworkedtogetherandrarelysoughthelpfromothersNewSchoolwereinclinedtowardsadiscontinuousstructureinnatureatthemostfundamentallevelandtoadoctrineofcomplementarybetweenoppositesDiscontinuousnesswasthelanguageusedbythesementodescribeatomicphenomenaNOTE Causalitywasnotthecentralquestioninthedevelopmentofthetheory NewSchool doesPhilosophy BecauseofthefailuresofsomeclassicalapproachesteamNewSchooltookupnewphilosophicalpositionsonwhatwaspossibleBohrbelievedthefailureoftheclassicalmechanicsexplainingtheelectrontheoryofmetalswasduetoaninsufficiencyintheclassicalprinciplesPauliwasconvincedthataContinuumFieldtheory withparticlesassingularities wasnotpossiblePauliandHeisenbergdecidedelectronorbitalsweremeaninglessbecauseofthefailuretoapplyoldquantumtheorytomolecularsystemsThereexistedacleardesiretorevolutionizetheconceptsofthetime From1924 1927HeisenbergworkedonhisversionofthequantummodelOfnotearehis operators whichhavetheunusualpropertythattheorderofmultiplicationmatters A B B Ausually WenowknowthisisusuallythecasewhenAandBare nxn matrices n 1 and isstandardmatrixmultiplicationThenewmathseemedmysteriousyetworkedextremelywell seemedpromising andforrealtherewerenootheralternativesThisnewmathisdiscrete asopposedtocontinuous whichappealedtoandsuitedwellNewSchool sunderstandingofthenatureoftheatom Team OldSchool turnright Einstein LouisdeBroglie andSchrodingerNotasclosedatTeamNewSchoolConsideredthecontinuouswaveasthebasicphysicalentitysubjecttoacausaldescriptionTeamOldSchoolavoidsthenotionofdiscontinuityandotherradicalideas makingthemteamOldSchool Einstein sinfluence Einsteinviewsthefoundationalquestionsofphysics suchasrelativity quantumtheory unifiedfieldtheory asthesearchforarational causalreasoningwhichcanbecomprehendedintermsofobjectivereality whichsuggestsacontinuityofbasicphysicalprocessesIn1909EinsteinusedBlackbodyradiationtoshowtheradiationexhibitedwaveandparticlebehaviorsHoweveraftershowingthatthedirectionamoleculehasafteremittingradiationislefttochance Einsteinproclaimeditamistakeofthetheory DeB