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1、Measurementinquantummechanics1MeasurementinquantummechanicsTheframeworkofquantummechanicsrequiresacarefuldefinitionofmeasurement.Theissueofmeasurementliesattheheartoftheproblemoftheinterpretationofquantummechanics,forwhichthereiscurrentlynoconsensus.MeasurementfromapracticalpointofviewMeasuremen
2、tisviewedindifferentwaysinthemanyinterpretationsofquantummechanics;however,despitetheconsiderablephilosophicaldifferences,theyalmostuniversallyagreeonthepracticalquestionofwhatresultsfromaroutinequantum-physicslaboratorymeasurement.Todescribethis,asimpleframeworktouseistheCopenhageninterpretatio
3、n,anditwillbeimplicitlyusedinthissection;theutilityofthisapproachhasbeenverifiedcountlesstimes,andallotherinterpretationsarenecessarilyconstructedsoastogivethesamequantitativepredictionsasthisinalmosteverycase.QualitativeoverviewThequantumstateofasystemisamathematicalobjectthatfullydescribestheq
4、uantumsystem.Onetypicallyimaginessomeexperimentalapparatusandprocedurewhich"prepares"thisquantumstate;themathematicalobjectthenreflectsthesetupoftheapparatus.Oncethequantumstatehasbeenprepared,someaspectofitismeasured(forexample,itspositionorenergy).Iftheexperimentisrepeated,soastomeasurethesame
5、aspectofthesamequantumstatepreparedinthesameway,theresultofthemeasurementwilloftenbedifferent.Theexpectedresultofthemeasurementisingeneraldescribedbyaprobabilitydistributionthatspecifiesthelikelihoodsthatthevariouspossibleresultswillbeobtained.(Thisdistributioncanbeeitherdiscreteorcontinuous,dep
6、endingonwhatisbeingmeasured.)Themeasurementprocessisoftensaidtoberandomandindeterministic.(However,thereisconsiderabledisputeoverthisissue;insomeinterpretationsofquantummechanics,theresultmerelyappearsrandomandindeterministic,inotherinterpretationstheindeterminismiscoreandirreducible.)Thisisbeca
7、useanimportantaspectofmeasurementiswavefunctioncollapse,thenatureofwhichvariesaccordingtotheinterpretationadopted.Whatisuniversallyagreed,however,isthatifthemeasurementisrepeated,withoutre-preparingthestate,onefindsthesamere
