苏汝铿高等量子力学讲义(英文版)Chapter4 Path Integral.ppt

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1、Chapter4PathIntegral§4.1ClassicalactionandtheamplitudeinQuantumMechanicsIntroduction:howtoquantize?WavemechanicshSchrödingerequ.MatrixmechanicshcommutatorClassicalPoissonbracketQ.P.B.Pathintegralhwavefunction§4.1ClassicalactionandtheamplitudeinQuantumMechanicsBasicideaInfiniteorbitsDiffer

2、entorbitshavedifferentprobabilities§4.1ClassicalactionandtheamplitudeinQuantumMechanicsAparticlestartingfromacertaininitialstatemayreachthefinalstatethroughdifferentpossibleorbitswithdifferentprobabilities§4.1ClassicalactionandtheamplitudeinQuantumMechanicsClassicalaction§4.1Classicalactionand

3、theamplitudeinQuantumMechanics§4.1ClassicalactionandtheamplitudeinQuantumMechanics§4.1ClassicalactionandtheamplitudeinQuantumMechanics§4.1ClassicalactionandtheamplitudeinQuantumMechanicsFreeparticle§4.1ClassicalactionandtheamplitudeinQuantumMechanics§4.1ClassicalactionandtheamplitudeinQuantumM

4、echanicsLinearoscillator§4.1ClassicalactionandtheamplitudeinQuantumMechanics§4.1ClassicalactionandtheamplitudeinQuantumMechanics§4.1ClassicalactionandtheamplitudeinQuantumMechanics§4.1ClassicalactionandtheamplitudeinQuantumMechanicsAmplitudeinquantummechanicsAllpaths,notonlyjustonepathfromatob

5、,havecontributionsThecontributionsofallpathstoprobabilityamplitudearethesameinmodule,butdifferentinphasesThecontributionofthephasefromeachpathisproportionaltoS/h,whereSistheactionofthecorrespondingpath§4.1ClassicalactionandtheamplitudeinQuantumMechanicsInsummary:thequantizationschemeofthepathi

6、ntegralsupposesthattheprobabilityP(a,b)ofthetransitionis§4.1ClassicalactionandtheamplitudeinQuantumMechanics§4.1ClassicalactionandtheamplitudeinQuantumMechanicshappearsasapartofthephasefactorQ.M.C.Mwhileh0§4.1ClassicalactionandtheamplitudeinQuantumMechanicsClassicallimit:S/h>>1Quicklyoscilla

7、te§4.1ClassicalactionandtheamplitudeinQuantumMechanicsSdependsonxa,xbconsiderably§4.2PathintegralHowtocalculateK(b,a)§4.2PathintegralKey:thevariableintheintegrationisafunctionThisisafunctionalintegral§4.2Pathintegral§4.2Pathintegral§4.