QMGreensite_merged
21.3. HILBERTSPACE 335 [J−]jm,j′m′ = √ (j′+m′)(j′−m′+1) ̄hδjj′δm,m′− 1 [J+]jm,j′m′ = √ (j′−m′)(j′+m′+1) ̄hδjj′δm,m′+1 (21.190) I ...
336 CHAPTER21. QUANTUMMECHANICSASLINEARALGEBRA Often,indealingwithproblemsinatomic,nuclear,orparticle physics, weare interested ...
21.4. CANONICALQUANTIZATION 337 and,inaddition,wemakethecrucialidentificationofx ̃andp ̃asthefollowingoper- ators,actingonfuncti ...
338 CHAPTER21. QUANTUMMECHANICSASLINEARALGEBRA weget <ψ| ∂H ∂P |ψ>=<ψ| 1 i ̄h [X,H]|ψ> (21.204) Likewise,thesecondEh ...
21.4. CANONICALQUANTIZATION 339 GiventhatH=H(P,X)canbeexpressedasapolynomialinXandP,therelation (21.207)follows. Tofindtheoperat ...
340 CHAPTER21. QUANTUMMECHANICSASLINEARALGEBRA Beginwithasystemwithasetofcoordinatesandmomenta{qa,pa},whosedy- namicsisdescribe ...
21.5. POISSONBRACKETS 341 and Qa[{q},{q′}] = qaδD(q−q′) Pa[{q},{q′}] = −i ̄h ∂ ∂qa δD(q−q′) (21.223) Usingthesematrixelementsint ...
342 CHAPTER21. QUANTUMMECHANICSASLINEARALGEBRA butofcourseonecouldalsoexpresstheLagrangianinsphericalcoordinatesr,θ,φ, andobtain ...
Chapter 22 The EPR Paradox and Bell’s Theorem Nomanisanisland... JohnDonne SupposewehaveabaseballinPhiladelphia,andafootballinDe ...
344 CHAPTER22. THEEPRPARADOXANDBELL’STHEOREM systemisinstate ψ(x 1 ,x 2 )=ψC(x 1 )ψD(x 2 ) (22.2) Butwhatdowemakeofthe(normalize ...
22.1. THEEPRPARADOX 345 affectthespinoftheotherparticle(”R”)ontheright,andyetweknowthat Ris spin-down,itmustbethatRwasspindownev ...
346 CHAPTER22. THEEPRPARADOXANDBELL’STHEOREM in totalcontradictionto the reported fact (B)!Conclusion: no experimentshould repor ...
22.2. BELL’STHEOREM 347 Nowifboth(A)and(B)aretrue,itmeansthatbeforeanymeasurementtakes place,RisneitherinstateβzR(asinstateψ 1 ) ...
348 CHAPTER22. THEEPRPARADOXANDBELL’STHEOREM Nolocalhiddenvariabletheorycanagreewithallofthepredictionsofquantum mechanics. Ther ...
22.2. BELL’STHEOREM 349 particlemusthavebeeninastatewhichwouldcauseatype 1 detectortoflashred. So,ifwesetbothswitchesto1,wewould ...
350 CHAPTER22. THEEPRPARADOXANDBELL’STHEOREM TherelevantexperimentswereperformedbyAspectandhiscollaboratorsinthe 1970s. Thetwopa ...
22.3. ENTANGLEDSTATESFOR”QUANTUMRADIO”? 351 where cnφn(x 2 )= ∫ dx 1 φ∗n(x 1 )Ψ(x 1 ,x 2 ) (22.24) Definedinthisway,thestates{φn ...
352 CHAPTER22. THEEPRPARADOXANDBELL’STHEOREM B’aresimultaneous,butAislaterthanBandB’.NotsointheRajiv-Fatimarest frame:forthem,ev ...
22.3. ENTANGLEDSTATESFOR”QUANTUMRADIO”? 353 Iftheright-handparticleisinstate|ψ>,theexpectationvalueforobservableQis <ψ|Q|ψ ...
354 CHAPTER22. THEEPRPARADOXANDBELL’STHEOREM = ∑ |bM|^2 <φM|Q|φM> = ∑ M [c∗RURM∗ <ψ|r+c∗GUGM∗ <ψ′|r]Q[cRURM|ψ>r+c ...
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