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1、第七章粒子在電磁場(chǎng)中的運(yùn)動(dòng)7.1)設(shè)帶電粒子在互相垂直的均勻電場(chǎng)和均勻磁場(chǎng)中運(yùn)動(dòng),求能級(jí)本征值和本征。(參《導(dǎo)論》)解:以電場(chǎng)方向?yàn)檩S,磁場(chǎng)方向?yàn)檩S,則,(1)去電磁場(chǎng)的標(biāo)勢(shì)和矢勢(shì)為,(2)滿足關(guān)系,粒子的Hamiton量為(3)取守恒量完全集為,它們的共同本征函數(shù)可寫成(4)其中和為本征值,可取任意函數(shù)。滿足能量本證方程:因此滿足方程(5)亦即,對(duì)于來(lái)說(shuō),和式等價(jià):(6)其中(7)式(6)相當(dāng)于一維諧振子能量算符再加上兩項(xiàng)函數(shù),因此本題能級(jí)為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)其中和為任意實(shí)數(shù),式(4)中為以為變量的一維諧振子能量本征函數(shù),即(9)為厄密多項(xiàng)式,。7.2)設(shè)帶電粒子在均勻磁場(chǎng)和各向同性諧振子勢(shì)中運(yùn)動(dòng),求能量本征值。第八章自旋8.1)在表象中,求的本征態(tài)。解:在表
7、象中,的矩陣表示為:設(shè)的本征矢(在表象中)為,則有可得及。則則利用歸一化條件,可求出的兩個(gè)本征態(tài)為。8.2)在表象中,求的本征態(tài),是方向的單位矢.解:在表象中,的矩陣表示為,,(1)因此,(2)replacingthesealingplateandboltscrewdown,checkthewatersurfaceandsupportstheslidersurfaceinheightmeetstherequirements,toensurethattheamountofcompression.8.2.5instal