量子力学发展史

量子力學發展史近代科學發展之三物理模型粒子模型•Allowedustoignoreunnecessarydetailsofanobjectwhenstudyingitsbehavior系統與剛體•Extensionofparticlemodel波動模型兩種新模型•量子粒子•邊界條件下的量子粒子黑體幅射物體在任何溫度下皆會發出熱幅射(電磁幅射)電磁幅射波長會隨物體表面溫度的變化而改變黑體為一理想系統會吸收所有射入的幅射由黑體發射出的電磁幅射稱為幅射黑體近似黑體模型可近似為開了一小孔洞的金屬空腔離開空腔的電磁幅射其性質將只與空腔的表面溫度有關黑體實驗結論幅射的總功率與溫度的關係滿足Stefan定律•Stefan’sLaw•P=sAeT4•Forablackbody,e=1sistheStefan-Boltzmannconstants=5.670x10-8W/m2.K4波長分佈曲線的峰值位置隨溫度升高兒而往短波長方向偏移，Wien位移定律•Wien’sdisplacementlawlmaxT=2.898x10-3m.K黑體幅射強度隨波長的分佈l幅射強度隨溫度升高而增強l總幅射量隨溫度升高而變大•Theareaunderthecurve峰值對應的波長隨溫度升高而變短紫外危機古典物理的預測與實驗在短波處的結果發生極大的差異此現象稱為紫外危機，尤其古典物理預測當幅射波的波長趨近於零時更會得到無限大的能量，此與實驗觀察完全相反MaxPlanck(拯救紫外危機的英雄)1858–1947Heintroducedtheconceptof“quantumofaction”In1918hewasawardedtheNobelPrizeforthediscoveryofthequantizednatureofenergyPlanck’sTheoryofBlackbodyRadiationIn1900,PlanckdevelopedastructuralmodelforblackbodyradiationthatleadstoanequationinagreementwiththeexperimentalresultsHeassumedthecavityradiationcamefromatomicoscillationsinthecavitywallsPlanckmadetwoassumptionsaboutthenatureoftheoscillatorsinthecavitywallsPlanck’sTheoryofBlackbodyRadiationIn1900,PlanckdevelopedastructuralmodelforblackbodyradiationthatleadstoanequationinagreementwiththeexperimentalresultsHeassumedthecavityradiationcamefromatomicoscillationsinthecavitywallsPlanckmadetwoassumptionsaboutthenatureoftheoscillatorsinthecavitywallsPlanck’sAssumption,1TheenergyofanoscillatorcanhaveonlycertaindiscretevaluesEn•En=nhƒ•nisapositiveintegercalledthequantumnumber•hisPlanck’sconstant•ƒisthefrequencyofoscillation•Thissaystheenergyisquantized•EachdiscreteenergyvaluecorrespondstoadifferentquantumstatePlanck’sAssumption,2TheoscillatorsemitorabsorbenergyonlyindiscreteunitsTheydothiswhenmakingatransitionfromonequantumstatetoanother•Theentireenergydifferencebetweentheinitialandfinalstatesinthetransitionisemittedorabsorbedasasinglequantumofradiation•AnoscillatoremitsorabsorbsenergyonlywhenitchangesquantumstatesEnergy-LevelDiagramAnenergy-leveldiagramshowsthequantizedenergylevelsandallowedtransitionsEnergyisontheverticalaxisHorizontallinesrepresenttheallowedenergylevelsThedouble-headedarrowsindicateallowedtransitionsCorrespondencePrinciple(對應原理)當量子系統的量子態總數變大時，量子現象應當會連續地轉變成古典現象•Quantumeffectsarenotseenonaneverydaybasissincetheenergychangeistoosmallafractionofthetotalenergy•QuantumeffectsareimportantandbecomemeasurableonlyonthesubmicroscopiclevelofatomsandmoleculesPhotoelectricEffectThephotoelectriceffectoccurswhenlightincidentoncertainmetallicsurfacescauseselectronstobeemittedfromthosesurfaces•TheemittedelectronsarecalledphotoelectronsTheeffectwasfirstdiscoveredbyHertzPhotoelectricEffectApparatusWhenthetubeiskeptinthedark,theammeterreadszeroWhenplateEisilluminatedbylighthavinganappropriatewavelength,acurrentisdetectedbytheammeterThecurrentarisesfromphotoelectronsemittedfromthenegativeplate(E)andcollectedatthepositiveplate(C)PhotoelectricEffect,ResultsAtlargevaluesofDV,thecurrentreachesamaximumvalue•AlltheelectronsemittedatEarecollectedatCThemaximumcurrentincreasesastheintensityoftheincidentlightincreasesWhenDVisnegative,thecurrentdropsWhenDVisequaltoormorenegativethanDVs,thecurrentiszeroPhotoelectricEffectFeature1Dependenceofphotoelectronkineticenergyonlightintensity•ClassicalPrediction•Electronsshouldabsorbenergycontinuallyfromtheelectromagneticwaves•Asthelightintensityincidentonthemetalisincreased,theelectronsshouldbeejectedwithmorekineticenergy•ExperimentalResult•Themaximumkineticenergyisindependentoflightintensity•ThecurrentgoestozeroatthesamenegativevoltageforallintensitycurvesPhotoelectricEffectFeature2Timeintervalbetweenincidenceoflightandejectionofphotoelectrons•ClassicalPrediction•Forveryweaklight,ameasurabletimeintervalshouldpassbetweentheinstantthelightisturnedonandthetimeanelectronisejectedfromthemetal•Thistimeintervalisrequiredfortheelectrontoabsorbtheincidentradiationbeforeitacquiresenoughenergytoescapefromthemetal•ExperimentalResult•Electronsareemittedalmostinstantaneously,evenatverylowlightintensities•Lessthan10-9sPhotoelectricEffectFeature3Dependenceofejectionofelectronsonlightfrequency•ClassicalPrediction•Electronsshouldbeejectedatanyfrequencyaslongasthelightintensityishighenough•ExperimentalResult•Noelectronsareemittediftheincidentlightfallsbelowsomecutofffrequency,ƒc•Thecutofffrequencyischaracteristicofthematerialbeingilluminated•NoelectronsareejectedbelowthecutofffrequencyregardlessofintensityPhotoelectricEffectFeature4Dependenceofphotoelectronkineticenergyonlightfrequency•ClassicalPrediction•Thereshouldbenorelationshipbetweenthefrequencyofthelightandtheelectrickineticenergy•Thekineticenergyshouldberelatedtotheintensityofthelight•ExperimentalResult•ThemaximumkineticenergyofthephotoelectronsincreaseswithincreasinglightfrequencyPhotoelectricEffectFeatures,SummaryTheexperimentalresultscontradictallfourclassicalpredictionsEinsteinextendedPlanck’sconceptofquantizationtoelectromagneticwavesAllelectromagneticradiationcanbeconsideredastreamofquanta,nowcalledphotonsAphotonofi