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1、第七章粒子在电磁场中的运动7.1)设带电粒子在互相垂直的均匀电场和均匀磁场中运动,求能级本征值和本征。(参《导论》)解:以电场方向为轴,磁场方向为轴,则,(1)去电磁场的标势和矢势为,(2)满足关系,粒子的Hamiton量为(3)取守恒量完全集为,它们的共同本征函数可写成(4)其中和为本征值,可取任意函数。满足能量本证方程:因此满足方程(5)亦即,对于来说,和式等价:(6)其中(7)式(6)相当于一维谐振子能量算符再加上两项函数,因此本题能级为replacingthesealingplateandboltscrewdown,checkthewatersurfaceandsu
2、pportstheslidersurfaceinheightmeetstherequirements,toensurethattheamountofcompression.8.2.5installationofhydraulicheadstockgearhingeinstallation:firstcylinderhingeseatbaseweldchipboard,hingesinplace,releaseheightmeasurementbytotalstationandtheCenter,horizontalcontrolpoints.Goodpoint,concen
3、tricitycontrolhingeandhingeseatelevation.Fueltankinstallation:whenthehingedseatsecondstageconcretestrengthtomeetthedesignrequirements,fueltankinstallation.Cylinderbeforeinstallation,cleanlineonthecylinderandcylinderconnectionandreinforcement.Cylinderandhingedconnections,weldingatemporarysu
4、pportthefueltankisfixed,sothatlaternoloadtest.Hydraulicinstallation:aftertheformationofheadstockgearroom,equipmentwillbeprovidedaccordingtothedesigndrawingsofhydraulicstationchannel,expansionbolts.8.2.6hoisttoinstallone-waydoorinstallation:carttravelingmechanisminplace,runninggearandbottom
5、beampositioningpositiontheconnectionofthefactoryiscompleted,50toncrawlercranetohoisttheminorbit,adjustlevels,spananddiagonal,finished,reinforced.Legsinstalled:legsandbeamscomposedofh-shaped,adjustthelegsafteropeningsizeconsistentwiththebottomendrailboltholedistance,tightboltswith50Tcraneho
6、isting.Adjustverticaldegrees,fixedwithchainandwirerope.Machineinstallation:twolegsaftertheinstallationprocessiscompletedandfullyfixed,formachineinstallation.Selectedchickenfarmsshould29(8)其中和为任意实数,式(4)中为以为变量的一维谐振子能量本征函数,即(9)为厄密多项式,。7.2)设带电粒子在均匀磁场和各向同性谐振子势中运动,求能量本征值。第八章自旋8.1)在表象中,求的本征态。解:在表
7、象中,的矩阵表示为:设的本征矢(在表象中)为,则有可得及。则则利用归一化条件,可求出的两个本征态为。8.2)在表象中,求的本征态,是方向的单位矢.解:在表象中,的矩阵表示为,,(1)因此,(2)replacingthesealingplateandboltscrewdown,checkthewatersurfaceandsupportstheslidersurfaceinheightmeetstherequirements,toensurethattheamountofcompression.8.2.5instal