【有人说：“在微观物理学中,由于我们不可能同时准确地知道某个粒子的位置和动量,粒子出现位置是无规律可循的.”请你对以上说法做出评论.江苏高中物理选修3-5第45页】
有人说：“在微观物理学中,由于我们不可能同时准确地知道某个粒子的位置和动量,粒子出现
位置是无规律可循的.”请你对以上说法做出评论.
江苏高中物理选修3-5第45页
Inquantummechanics,theHeisenberguncertaintyprinciplestatesthatcertainpairsofphysicalproperties,likepositionandmomentum,cannotbothbeknowntoarbitraryprecision.Thatis,themorepreciselyonepropertyisknown,thelesspreciselytheothercanbeknown.Thisisnotastatementaboutthelimitationsofaresearcher'sabilitytomeasureparticularquantitiesofasystem,itisastatementaboutthenatureofthesystemitselfasdescribedbytheequationsofquantummechanics.Accordingtotheuncertaintyprinciple,itis,forinstance,impossibletomeasuresimultaneouslybothpositionandvelocityofamicroscopicparticlewithanydegreeofaccuracyorcertainty.
Inquantummechanics,aparticleisdescribedbyawave.Thepositionoftheparticleisregardedasbeingwherethewaveamplitudeisgreatestandthemomentumisdeterminedbythewavelength.Thepositionisuncertaintothedegreethatthewaveisspreadout(well-definedwavelength),butthemomentumiscertain(well-defined)onlytothedegreethatthewavelengthiswell-defined.Thus,positionandmomentumforaparticlehaveoppositerequirementsforgooddefinition,sothatbothpositionandwavelengthcannotsimultaneouslybewell-defined.
Theonlykindofwavewithadefinitepositionisconcentratedatonepoint,andsuchawavehasanindefinitewavelength.Conversely,theonlykindofwavewithadefinitewavelengthisaninfiniteregularperiodicoscillationoverallspace,whichhasnodefiniteposition.Soinquantummechanics,therearenostatesthatdescribeaparticlewithbothadefinitepositionandadefinitemomentum.Themoreprecisetheposition,thelessprecisethemomentum.
Theuncertaintyprinciplecanberestatedintermsofmeasurements,whichinvolvescollapseofthewavefunction.Whenthepositionismeasured,thewavefunctioncollapsestoanarrowbumpnearthemeasuredvalue,andthemomentumwavefunctionbecomesspreadout.Theparticle'smomentumisleftuncertainbyanamountinverselyproportionaltotheaccuracyofthepositionmeasurement.Theamountofleft-overuncertaintycanneverbereducedbelowthelimitsetbytheuncertaintyprinciple,nomatterwhatthemeasurementprocess.
Thismeansthattheuncertaintyprincipleisrelatedtotheobservereffect,withwhichitisoftenconflated.Theuncertaintyprinciplesetsalowerlimittohowsmallthemomentumdisturbanceinanaccuratepositionexperimentcanbe,andviceversaformomentumexperiments.
Amathematicalstatementoftheprincipleisthateveryquantumstatehasthepropertythattherootmeansquare(RMS)deviationofthepositionfromitsmean(thestandarddeviationoftheX-distribution):
timestheRMSdeviationofthemomentumfromitsmean(thestandarddeviationofP):
canneverbesmallerthanafixedfractionofPlanck'sconstant:
Anymeasurementofthepositionwithaccuracycollapsesthequantumstatemakingthestandarddeviationofthemomentumlargerthan.