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1、MonaLisa-ineffablesmileofquantummechanicsSlobodanPrvanovi´cInstituteofPhysics,P.O.Box57,11080Belgrade,SerbiaAbstractTheportraitofMonaLisaisscrutinizedwithreferencetoquan-tummechanics.Theelementsofdifferentexpressionsarefirstlyrecog-nizedonherface.Thecontradictory
2、detailsarethenclassifiedintwopicturesthat,undoubtedlyrepresentingdistinctmoods,confirmdi-chotomouscharacteroftheoriginal.ConsecutivediscussionhasleadtoconclusionthatthemysteriousstateMonaLisaisinactuallyiscoherentmixture-superposition,ofcheerfulnessandsadness.St
3、ateofthephysicalsystemisamongthemostimportantconceptsofquantummechanics.Beingtheprimitiveconceptofthetheory,itisusuallyleftundefined.However,bystatewemeanalistofsomerelevantcharac-teristicsofthesysteminquestion.Moreorlessexactinformationaboutthequantitiespertai
4、ningtothesystemareonthislist,tellingushowitisprepared.Foroperationalreasons,stateofthequantummechanicalsystemisrepresentedbysomevectoroftheHilbertspace.Precisely,raysrepresentstates,whilequantitiesarerepresentedbytheHermitianoperatorsactinginthisHilbertspaceof
5、states.ThespectraldecompositionoftheHermitianoperator,inthesimplestpossiblecasewhenthespectrumisdiscreteandnondegenerate,reads:arXiv:physics/0302089v1[physics.pop-ph]25Feb2003XNAˆ=ai
6、aiihai
7、,(1)i=1whereNisdimensionofHilbertspace.InthisexpressionwehaveusedDirac
8、notation:
9、aiihai
10、istheprojectoronthevector
11、aii-aformalrepresentative1ofthestate.Therealnumbersai,beingtheeigenvalues-characteristicvalues,oftheoperatorAˆ,representpossiblenumericalrealizationsofsomequantity(whichisrepresentedabovebyAˆ).Here,weareinterestedonly
12、inonequantity-observable,andtoeachofitsquantitativerealizationsaitherecorrespondsappropriatestateofthesystemdescribedby
13、aiiandprojector
14、aiihai
15、.Measurementisaprocessofacquisitionofknowledgeaboutthevalueofsomeobservableandaboutthestateofthesystem.Measurementsar
16、eper-formedbysomespeciallydesignedand,usuallycomplicatedphysicalsystems-apparatus.Theyinteractwithmeasuredsystemsand,ontheotherside,displaynumbersasresults.Andastheresultofparticul
