狄拉克符号的教法

2000191()JournaloftheCUN(NaturalSciencesEdition)Jan.2000Vol.9No.1X(,100081),.,1:;;;;1,..,,.:?,É[1]194:ûW=6kkûWûk=6kûkkûW.(1)kûûW,ûk.ûk,ûk,ûk,.,,ûkkû,ûW?,?.[2],.,.,.,..2,[2].,AWA,AûAAû,ûAAû.BWB,BûBX:1998-08-10Bû,ûBBû.Qd,u1,u2,un,,WAun,WA=6nanun1(2)QA1k(k)7A,7A=a1a2anak;(3)k1,70A=[a31a32a3na3k].(4),7Bun,7B=6nbnun.(5)QB7B=b1b2bnbk(6).70B=[b31b32b3nb3k].(7),AûBûQ,ûAûBQ.(3)(6),(4)(7).Qdûn,,:û1=100,û2=010,ûn=010n,(8):Qdun(2)(5)un=6iDniui.(9)06()93.BûûAûABû,[2]:BûA=a1b31+a2b32++anb3n+=6nanb3n.(10)Bû(7),ûA(3),BûA(7)(3),[b31b32b3n]a1a2an=6nanb3n,(11)(10).,,.[3].[2].Éûkkû[1],.ûABû(3)(7),ûABû:a1a2an[b31b32b3n]=a1b31a1b32a1b3na2b31a2b32a2b3nanb31anb32anb3n(12)(12)ûABûQ.ûnnû,,:nn1,.ûnnû=0010[0010]=0000000000100000n(13)n,.,161:,.,,,;,.,.,,..,A,BC,ABC=(AB)C=A(BC).(14),,[3].,,[2].,(1).kûûWkûW,ûkûk,(1).(1),ûkkûûW,.kûûW(),ûk;ûkkû,ûkkû,ûW,ûk(kûW)=(ûkkû)ûW.(15)4Q,ûAQdûn:ûA=6nanûn1(16)(3)(8),nûûAnûA=6iaiDni=an,(17)(16)ûA=6nnûAûn=6nûnnûA,(18)6nûnnû=1,(19)1.ûn.(415-15)(19),1,.Qd,,ûqq.,,Qd6nûnnû+dqûqqû=11(20)Qd,(20).,ûxdxûxxû=1.(21)26()9ûpdpûppû=1.(22)ûAûx,(18),ûA=dxûxxûA.(23)BûûABûA=dxBûxxûA=dxW3B(x)WA(x).(24)FdûAûB,ûB=FdûA.(25)ûAûB1k,Fdkk.Qd,(18)ûB=6nûnnûB.(26)(18)(26)(25),6nûnnûB=6nFdûnnûA.(27)mûmûn=Dmn,nûB=6nmûFûnnûA,(28)mûFûnFdQFmn.(28)bm=6nFmnan.(29)ûB,FdûA,(25).F(3),(3)F,Bû=AûF01(30)(30)(25).Fd,F=F0,(30)Bû=AûF.(31)5,Q,.,.(19)1,.,,.1.(É).:,1995,1921982..:,1995,1191243P.A.M.Dirac,ThePrinciplesofQuantumMechanics(4thed.),(OxfordattheClarendonPress,361:1958),1826AMethodofTeachingDiracSymbolsZhuZhenhe(DepartmentofPhysics,CentralUniversityforNationalities,Beijing100081)AbstractAmethodofteachingDiracsymbolsthattheabstractisrepresentedbythespecificispresented.Aketvectorandabravectorcanberegardedasacolumnmatrixandarowmatrix,respectively.Theproductofaketvectorandabravectorwiththeketontheleftisdefined.Theassociativeaxiomofmultiplicationforthecontinuedproductofketsandbrasisstated.Keywords:Diracsymbols;ketvector;bravector;matrix;associativeaxiomofmultiplication(58)OnMultiplicationofVectorandTensorZhuZhengyuan(DepartmentofMathematics,CentralUniversityforNationalities,Beijing100081)AbstractInthispaper,Westudysomemultiplicationesofvectorandtensorincludingdefinitions,propertiesandrelationbetweenthem.Keywords:Scalar(inner)product;vectorproduct;mixedproduct;tensorproduct;exterior(outer)product46()9