wave packet的物理意义.doc

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1、Inphysics,awavepacketisanenvclopeorpacketcontaininganumberofplanewaveshavingdifferentwavenumbersorwavelengths,chosensuchthattheirphasesandamplitudesinterfereconstructivelyoverasmallregionofspace.Dependingontheevolutionequation,whilepropagatingthewavepacket'senvelopemay

2、remainconstant(nodispersion,seefigure)oritmaychange(dispersion).Inquantummechanicstothewavepacketaspecialsignificanceisascribed:itisinterpretedtobea/zprobabilitywave"describingtheprobabilitythataparticleorparticlesinaparticularstatewillbemeasuredtohaveagivenpositionand

3、momentum.Itisinthiswaysimilartothewavefunction.ByapplyingtheSchr6dingerequationinquantummechanicsitispossibletodeducethetimeevolutionofasystem,similartotheprocessoftheHami]tonianformalismincldssicdlmechdriics.ThewavepacketisamathematicalsolutiontotheSchrodingerequation

4、.Thesquareoftheareaunderthewavepacketsolutionisinterpretedtobetheprobabilitydensityoffindingtheparticleinaregion.ThedispersivecharacterofsolutionsoftheSchrodingerequationhasplayedanimportantroleinreject!SchrNlingor'soriginalinterpretation,andacceptingtheBornrule.Inthec

5、oordinaterepresentationofthewave(suchastheCartesiancoordinatesystem)thepositionofthewaveisgivenbythepositionofthepacket.Moreover,thenarrowerthespatialwavepacket,andthereforethebetterdefinedthepositionofthewavepacket,thelargerthespreadinthemomentumofthewave.Thistrade-of

6、fbetweenspreadinpositionandspreadinmomentumisoneexampleoftheHeisenberguncertdintyprinciple.BackgroundIntheearly1900sitbecameapparentthatclassicalmechanicshadsomemajorfailings.IsaacNewtonoriginallyproposedtheideathatlightcameindiscretepacketswhichhecalled"corpuscles",bu

7、tthewave-likebehaviorofmanylightphenomenaquicklyledscientiststofavorawavedescriptionofelectronmgnetisin.Itwasn'tuntilthe1930sthattheparticlenatureoflightreallybegantobewidelyacceptedinphysics.Thedevelopmentofquantummechanics一anditssuccessatexplainingconfusingexperiment

8、alresults一wasatthefoundationofthisacceptance.Oneofthemostimportantconceptsintheformulationofquantummechanicsistheidea