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1、Chapter1Preface:Quantummechanicsandatomicphysicsreview1.1IntroductionInthiscourse,wewillapproachthe?eldofatomicphysicsbypresentingauni?edpictureofcoherentevolutionandenvironmentaldecoherenceanddissipation.Thecoursewilldeveloparoundthreethemes:?rstly,wewillelucidatetheoreticaltech
2、niquesforsimultaneouslytreatingbothcoherentanddissipativeprocesses.Wewillalsoconsiderexperimentalmethodsforstudyingatomicsystems,including,forexamplediscussionofhighresolutionspectroscopy,lasertrappingandcoolingandpreparationofquantumstatesofions.Finally,wewillincorporateexamples
3、whichillustratehowtheseexperimentalandtheoreticaltechniques?ndapplicationincurrentresearch.Thebasicphilosophyofthecourseistodevelopatheoreticalunder-standingof”simple”systems?rst,thatissystemswhereonlyafewstates,afewparticles,orafewquantaarerelevant.Thiswillleadustoexploresomenon
4、-trivialquantumdynamicsandstudythepossibilityofcontrollingrealisticquantumsystems,includingimperfectionsin”realworld”experi-ments.Oncethesebasicbuildingblocksaremastered,wewillconsidermorecomplexsystemsbycombiningelementswealreadyunderstandatabasicphysicallevel.Tounderstandthedyn
5、amicsofthesystemswewillstudyinthiscourse,wewillneedtotreatbothdissipationandcoherentquantumevolutiononanequalfooting.11.2Reviewofquantummechanics1.2.1StatesWebrie?yreviewbasicquantummechanicsandsomeelementaryresultsofatomicphysics.Themostcompleteknowledgeofthesystemiscontainedint
6、hestatevector
7、ψi,whichisanelementofaHilbertspaceH.Wecanexpandthestatevector
8、ψiinanyorthonormalbasis{
9、ni}oftheHilbertspace,X
10、ψi=
11、nihn
12、ψi.(1.1)nForconvenience,wewritecn=hn
13、ψifortheprojectionofthestate
14、ψionthebasisstate
15、ni,whichgivesustheexpansioncoe?cientsofthestate
16、ψiinthebasis{
17、n
18、i}.Theprobabilityof?ndingthesysteminthestate
19、niisthenPn=
20、cn
21、2.1.2.2Superpositions-InterferenceQuantummechanicsallowsforsuperpositionsofstates,inparticular,fortwostatesX
22、ψi=c(1)
23、niand(1.2)1nnX
24、ψi=c(2)
25、ni,(1.3)2nntheirsuperposition√1(
26、ψi+
27、ψi)hastheuniquepropertythattheproba-122bili
28、tyofbeinginstate
29、niisnotingeneralgivenby
