苏汝铿高量课件1234章.ppt

1、QuantumMechenicsII,Ru-KengSu2005.1.5,Chapter1FoundationofQuantumMechanics,1.1Statevector,wavefunctionandsuperpositionofstates,Thischapterevolvesfromanattemptofabriefreviewoverthebasicideasandformulaeinundergraduate-levelquantummechanics.Thedetailsofthischaptercanbefoundintheusualreferencesofquantumm

2、echanics,1.1Statevector,wavefunctionandsuperpositionofstates,1.1Statevector,wavefunctionandsuperpositionofstates,1.1Statevector,wavefunctionandsuperpositionofstates,1.2Schrdingerequationanditssolutions,1.2Schrdingerequationanditssolutions,1.2Schrdingerequationanditssolutions,1DSchrdingerequationInfi

3、nitepotentialwell,1.2Schrdingerequationanditssolutions,Infinitepotentialwell,1.2Schrdingerequationanditssolutions,Harmonicoscillator,1.2Schrdingerequationanditssolutions,Harmonicoscillator,1.2Schrdingerequationanditssolutions,Harmonicoscillator,1.2Schrdingerequationanditssolutions,Harmonicoscillator

4、,1.2Schrdingerequationanditssolutions,Harmonicoscillator,1.2Schrdingerequationanditssolutions,3DSchrodingerequationCentralpotential,1.2Schrdingerequationanditssolutions,Centralpotential,1.2Schrdingerequationanditssolutions,Coulombpotential,1.2Schrdingerequationanditssolutions,Coulombpotential,1.3Ope

5、rators,AccordingtotheBornstatisticalinterpretation,Theprobabilityoffindingaparticleatpositionrisjustthesquareofitswavefunction,1.3Operators,1.3Operators,1.3Operators,1.3Operators,pi-ih/2iCartesianrectangularcoordinates1stconvention:purecoordinatepartpuremomentumpart2ndconvention:mixedpart,1.3Operato

6、rs,1.3Operators,Commutator,1.3Operators,Commutator,1.3Operators,Commutator,1.3Operators,Hermitianoperator,1.3Operators,Eigenequation,1.3Operators,O-representation,1.3Operators,O-representation,1.4Approximationmethod,PerturbationindependentoftimeNon-degenerate,1.4Approximationmethod,Non-degenerate,1.

7、4Approximationmethod,Non-degenerate,1.4Approximationmethod,Degenerate,1.4Approximationmethod,Degenerate,1.4Approximationmethod,Advantagesofthischoiceare,1.4Approximationmethod,Degeneracymayberemoved,1.4Approximationmethod,PerturbationdependingontimeKey:Howtocalculatethetransitionamplitude,1.4Approxi

8、mationmethod,Perturbationdependingontime,1.4Approximationmethod,Perturbationdependingontime,1.4Approximationmethod,VariationalmethodKey:Howtochoosethetrialwavefunction,1.4Approximationmethod,Variationalmethod,1.5WKBmethod(Wentzel-Kramers-Brillouin),Basicidea:(Q.M.)(C.M)whenh0WKBSemi-Classicalmethod:

9、TofindanexpansionofhandsolvestationarySchrdingerequation,1.5WKBmethod(Wentzel-Kramers-Brillouin),1.5WKBmethod(Wentzel-Kramers-Brillouin),1.5WKBmethod(Wentzel-Kramers-Brillouin),For1Dcase,1.5WKBmethod(Wentzel-Kramers-Brillouin),For1Dcase,1.5WKBmethod(Wentzel-Kramers-Brillouin),For1Dcase,1.5WKBmethod(

10、Wentzel-Kramers-Brillouin),Threeregions:EU(x),1.5WKBmethod(Wentzel-Kramers-Brillouin),Conservationoftheprobability,1.5WKBmethod(Wentzel-Kramers-Brillouin),E=U(x)Turningpoints:Thesemi-classicalapproximationisnotapplicable,1.5WKBmethod(Wentzel-Kramers-Brillouin),E=U(x),1.5WKBmethod(Wentzel-Kramers-Bri

11、llouin),E=U(x),1.5WKBmethod(Wentzel-Kramers-Brillouin),EU(x),1.5WKBmethod(Wentzel-Kramers-Brillouin),a1,b1region,1.5WKBmethod(Wentzel-Kramers-Brillouin),EU(x),Asymptoticsolutions,1.5WKBmethod(Wentzel-Kramers-Brillouin),1.5WKBmethod(Wentzel-Kramers-Brillouin),1.5WKBmethod(Wentzel-Kramers-Brillouin),b

12、2,a2region,1.5WKBmethod(Wentzel-Kramers-Brillouin),ThisistheBohr-Sommerfeldquantizedcondition,1.5WKBmethod(Wentzel-Kramers-Brillouin),Example2:Barrierpenetration,1.5WKBmethod(Wentzel-Kramers-Brillouin),Barrierpenetration,1.5WKBmethod(Wentzel-Kramers-Brillouin),Barrierpenetration,1.5WKBmethod(Wentzel

13、-Kramers-Brillouin),Barrierpenetration,1.5WKBmethod(Wentzel-Kramers-Brillouin),Barrierpenetration,1.5WKBmethod(Wentzel-Kramers-Brillouin),Connectionformulae(dU/dx0),1.5WKBmethod(Wentzel-Kramers-Brillouin),Connectionformulae(dU/dx0),1.6Densitymatrix,Problem:Canwegetanewformulatocalculatetheexpectatio

14、nvaluelikequantumstatisticsQ.M.=Q.S.=tr(A)=tr(exp(-H)A),1.6Densitymatrix,Key:Whatisdensitymatrix,1.6Densitymatrix,Example:Twolevelsystem,1.6Densitymatrix,Example:Twolevelsystem,1.6Densitymatrix,PropertiesofdensitymatrixHermitianmatrix,1.6Densitymatrix,Propertiesofdensitymatrix,1.6Densitymatrix,Prope

15、rtiesofdensitymatrix,1.6Densitymatrix,PropertiesofdensitymatrixTheeigenvalueofdensitymatrixare0or1,1.6Densitymatrix,PropertiesofdensitymatrixTensorProduct,1.6Densitymatrix,Propertiesofdensitymatrix,1.6Densitymatrix,Propertiesofdensitymatrix,1.6Densitymatrix,PropertiesofdensitymatrixEvolutionequation

16、ofdensitymatrix,1.6Densitymatrix,PropertiesofdensitymatrixVectorpisapolarizationvectorofthestatewhichpointsindirection,1.6Densitymatrix,Propertiesofdensitymatrix,1.7CoherentStates,ConsideraforcedlinearHarmonicoscillator,1.7CoherentStates,1.7CoherentStates,ThelastequationcanbesolvedbyGreensfunctions,

17、1.7CoherentStates,1.7CoherentStates,whereainisthesolutionofthecorrespondinghomogeneousequationwhentt2Supposef(t)0whent1out,inparticular,tofindoutin,1.7CoherentStates,1.7CoherentStates,1.7CoherentStates,S|0isthecoherentstates,1.7CoherentStates,1.7CoherentStates,1.7CoherentStates,Propertiesofcoherents

18、tatesCoherentstatesistheeigenstateofoperatora,1.7CoherentStates,PropertiesofcoherentstatesCoherentstatesistheeigenstateofoperatora,1.7CoherentStates,Normalization,butdonotorthogonal,1.7CoherentStates,Normalization,butdonotorthogonal,1.7CoherentStates,Overcompleteset,1.7CoherentStates,Overcompleteset

19、,1.7CoherentStates,Overcompleteset,1.7CoherentStates,Coherentstateisthestatewhichsatisfiestheminimumuncertaintyprinciple,1.7CoherentStates,1.7CoherentStates,1.7CoherentStates,1.7CoherentStates,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,Schrdingerpicture(Labcoordinates),1.8Schrdinger

20、picture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,uns(x)doesnotdependontOsdoesnotdependontsdependsont,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,Heisenbergpicture(co-movingcoordinates),1.8Schrdingerpicture,Heisenbergpictureand

21、interactionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,unH(x,t)dependontOH(t)dependontHdoesnotdependont,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,Discussion:,1.8Schrdingerpicture,Heisenbergpicturean

22、dinteractionpicture,=,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,Forenergyrepresentation,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerp

23、icture,Heisenbergpictureandinteractionpicture,InteractionalpictureTofutherstudyperturbation,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenb

24、ergpictureandinteractionpicture,Tofindtheevolutionoperator,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,1

25、.8Schrdingerpicture,Heisenbergpictureandinteractionpicture,Chapter2ManyBodyProblem,2.1Secondquantization,Theidenticalparticlescannotbedistinguished,2.1Secondquantization,Theessenceoftheidenticalprincipleisthatthestateofasystemshouldbedescribedintermsoftheparticlenumberinacertainquantumstateandtheman

26、y-bodyproblemshouldbediscussedintheparticlenumberrepresentationinsteadoftheoriginalcoordinaterepresentation,2.1Secondquantization,Weneedtointroducethecreationandtheannihilationoperatorstodealwithvariousprobleminthemany-bodysystem,2.1Secondquantization,Bosesystem,2.1Secondquantization,2.1Secondquanti

27、zation,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,DiscussionsThewavefunctionisalreadysymmetricnkistheparticlenumberoperatorofkstate,2.1Secondquan

28、tization,2.1Secondquantization,2.1Secondquantization,Secondquantization,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,ForFermions,2.1Secondquantization,2.1Secondquantization,2.1Secondquantization,2.2Hartree-Forkmeanfieldapproximation,Ke

29、y:two-bodyproblem“one-bodyproblem”+“meanfield”Example:Freeelectrongasinthemetal,2.2Hartree-Forkmeanfieldapproximation,ScreeningCoulombpotential,Positivechargebackgroundcancelsk=0part,2.2Hartree-Forkmeanfieldapproximation,2.2Hartree-Forkmeanfieldapproximation,2.2Hartree-Forkmeanfieldapproximation,2.2

30、Hartree-Forkmeanfieldapproximation,2.2Hartree-Forkmeanfieldapproximation,2.2Hartree-Forkmeanfieldapproximation,2.2Hartree-Forkmeanfieldapproximation,Spineffect,2.2Hartree-Forkmeanfieldapproximation,2.2Hartree-Forkmeanfieldapproximation,2.2Hartree-Forkmeanfieldapproximation,2.3Superconductivetheory,2

31、.3Superconductivetheory,FrohlischHamiltonian:e-p-einteractione-eattractionCooperpair:BCSTheory(Variationalmethod),Variationalwavefunction,2.3Superconductivetheory,2.3Superconductivetheory,2.3Superconductivetheory,2.3Superconductivetheory,2.3Superconductivetheory,Bogoliubov-Valatincanonicaltransforma

32、tion,2.3Superconductivetheory,2.3Superconductivetheory,2.3Superconductivetheory,2.3Superconductivetheory,2.3Superconductivetheory,Energygapequation,2.3Superconductivetheory,2.3Superconductivetheory,2.3Superconductivetheory,2.3Superconductivetheory,Stablestate,2.4Landauphasetransitiontheory,Ehrenfest

33、equation,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,VanLauecriticismCan2ndorderphasetransitionexist?,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,2.4Landauphasetransitiont

34、heory,2.4Landauphasetransitiontheory,LandautheoryIntroducing“orderparameter”,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,min,stablemax,instalblephasetransitionpoint,2.4Landauphasetransitiontheory,real,stableimg,forbidden

35、,A0,2.4Landauphasetransitiontheory,LandautheoryEhrenfestequation,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,2.4Landauphasetransitiontheory,2.5Superfluiditytheory,LandausuperfluiditytheoryNewidea:elementaryexcitation,2.5Superfluiditytheory,Experiments

36、:Superfluidity10-510-4cm(0)Mendelsoneffect-point,2.5Superfluiditytheory,2.5Superfluiditytheory,Landautheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,Bogoliub

37、ovapproximatesecond-quantizationmethod,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,2.5Superfluiditytheory,Chapter3

38、RelativisticQuantumMechanics,Introduction,Non-relativisticquantummechanicsrelativisticquantummechanicsSchrdingerequationKlein-GordonequationSintegerDiracequationShalfintegerSpinisautomaticallycontainedinDiracequation,3.1KleinGordonequation,Lorentztransormationtime,spaceareofthesameweightKGequation,3

39、.1KleinGordonequation,3.1KleinGordonequation,3.1KleinGordonequation,3.1KleinGordonequation,DiscussionNegativeenergyinstable,3.1KleinGordonequation,Negativeprobability,3.1KleinGordonequation,3.1KleinGordonequation,Non-relativisticlimit:K-GeqScheq,3.1KleinGordonequation,3.1KleinGordonequation,3.1Klein

40、Gordonequation,Withelectromagneticfield,3.1KleinGordonequation,3.1KleinGordonequation,Covariantform,3.1KleinGordonequation,3.1KleinGordonequation,3.1KleinGordonequation,3.2Diracequation,Howtoovercomethenegativeprobabilitydifficulty,3.2Diracequation,3.2Diracequation,3.2Diracequation,3.2Diracequation,

41、Theconditionforand1)Theymustfollowtherelation2)OperatorHmustbeHermitian3)Lorentzinvariance,3.2Diracequation,3.2Diracequation,3.2Diracequation,3.2Diracequation,4anti-commutematricesand44matrices,3.2Diracequation,3.2Diracequation,Conservationlawoftheprobabilityflux,3.2Diracequation,3.2Diracequation,3.

42、3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,DiscussionPositiveenergystate(=+

43、1)Negativeenergystate(=-1)Eigenstatesofmomentump,3.3solutionsofthefreeparticle,Orbitalangularmomentumisnotconserved,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,Spinangularmomentum,Or,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,3.3solution

44、softhefreeparticle,Helicityoperator,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,If,wefind,Eigenvalues:,3.3solutionsofthefreeparticle,Eigenstates:,3.3solutionsofthefreeparticle,3.3solutionsofthefreeparticle,DiracholetheoryDiracseaHole:(+Ep0,+m0,+e0)(positron)1932,Andersondiscoveredpos

45、itronfromcosmicrayusingcloudchamber,3.4Diracequationinthecentralforcefield,Equationinnon-relativisticlimit,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,Innon-relativisticapproximation,3.4Diracequationinthecentralforcefield,3.4Di

46、racequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,Noting:uptotheorderNormalizationconditionmustbeensured,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequation

47、inthecentralforcefield,3.4Diracequationinthecentralforcefield,Byusing,3.4Diracequationinthecentralforcefield,Relativisticcorrectionofkineticenergy,3.4Diracequationinthecentralforcefield,Thomasterm,Darwinterm,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,QuantumnumberK

48、,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentr

49、alforcefield,3.4Diracequationinthecentralforcefield,Radialequations,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,3.4Diracequationinthecentralforcefield,Wetake,3.5SolutionoftheDiracequationintheCoulombfield,MotivationDiscussionth

50、eHydrogenatomFinestructure,3.5SolutionoftheDiracequationintheCoulombfield,3.5SolutionoftheDiracequationintheCoulombfield,3.5SolutionoftheDiracequationintheCoulombfield,3.5SolutionoftheDiracequationintheCoulombfield,3.5SolutionoftheDiracequationintheCoulombfield,3.5SolutionoftheDiracequationintheCoul

51、ombfield,n=0,1,2,n=1,2,3,3.5SolutionoftheDiracequationintheCoulombfield,3.5SolutionoftheDiracequationintheCoulombfield,Groundstate1S1/2(n=0,=-1,n=1,j=1/2),3.5SolutionoftheDiracequationintheCoulombfield,3.5SolutionoftheDiracequationintheCoulombfield,3.5SolutionoftheDiracequationintheCoulombfield,Ques

52、tionDiraceq+non-relativisticlimitScheqZ137?NolimitforZUniformchargedsphere?NolimitforZFinestructureEnjEnforScheq,3.6Kleinparadox,Anotherquestionforthenon-relativisticlimitofDiracequationDoespositronexistScalarlikepotentialandvectorlikepotential,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,Atthein

53、finity,thewavefunctionisnotzero,whichmeansthatthereisonlythescatteringstatesolutioninsteadofboundstatesolution,3.6Kleinparadox,3.6Kleinparadox,ThephysicsofKleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6K

54、leinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,Ifp=mc,3.6Kleinparadox,TheexplanationofKleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.6Kleinparadox,3.7MITbagmodel,Motivation:ca

55、nweestablishamodeltoconfinequarkscalarlikepotential,3.7MITbagmodel,3.7MITbagmodel,3.7MITbagmodel,Introducingscalarlikepotential,3.7MITbagmodel,3.7MITbagmodel,3.7MITbagmodel,Whenggwefindaexponentiallydecayingsolution,3.7MITbagmodel,Solutionofstepfunction,3.7MITbagmodel,3.7MITbagmodel,3.7MITbagmodel,3.7MITbagmodel,3.7MITbagmodel,3.7MITbagmodel,3.7MITbagmodel,Chapter4PathIntegral,4.1Classicalacti