角动量算符的本征态和转动矩阵的新形式.pdf

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1、第29卷第2期成都信息工程学院学报V01．29No．22014年4月JOURNALOFCHENGDUUNIVERSITYOFINFORMATIONTECHNOLOGYApr．2014文章编号：1671—1742{2014}02-0199—03NewExpressionsforBoththeRotationMatrixandEigenfunctionofAngularMomentumOperatorYANGJin．YUWan-Lun(SchoolofOptics&Electronics，CUIT，Chengdu610225，China)A

2、bstract：Therotationmatrixofangularmomentumoperatorplaysanelementaryandimportantroleintheoryofangularmomentum；ithasbeenderivedbymeansofvariousmethods．Weproposeanovelal—ternativeapproachtostudytheproblemofboththerotationmatrixandEigen-．functionofallgularmo．mentumoperator．B

3、yuseoftherelevantformulasandthedisentanglingformulaofSU(2)algebragen-eratorsofangularmomentum，thenewexpressionsfortheEigen-functionsofarbitrarycomponentofangularmomentumoperatoraredirectlyderived．ByusingtheseEigen-functions，thenewrotationmatrixrepresentationofangularmome

4、ntumoperatorisobtainedeasily．Itclearlyshowsthatourap—proachismuchsimpleranddirectonecomparedwithallthepreviousmethods．Keywords：quantummechanics；angularmomentumoperator；rotationalmatrixandEigen-function；operatordisentanglingmethodCLCnumber：0413．1Documentcode：A1Introductio

5、nAsiswellknown，therotationmatrixofangularmomentum，alsocalledtheDfunction，occurswidelyinquan—tumphysicsfieldssuchasmolecularandatomicnucleusrotation，etc，andhasbeenderivedbymakinguseofavarietyofabstractorcomplicatedmethods．TheseincludetheirreduciblerepresentationsofSU(2)an

6、dSO(3)algebras【卜引，thespinorrepresentationofangularmomentum[，Jordanmap[6。，coherent—statemethod[7。andsomeothermeth—ods[一9。．WiththeaidoftheSchwingerbosonrealizationofangularmomentumandcoherent．staterepresentation，Faneta1．obtainedthenormal—orderingproductofrotationoperator，f

7、romwhichtheDfunctionofrotationmatrixwasderived．Someyearsago．Wueta1．[o]presentedanovelformalismforsolvingenergyeigenvalueproblemswiththeHamiltonianstobeexpressedasafunctionofa~ngularmomentum．Basedontheformalism，theyobtmnedtheexplicitlyanalyticalexpressionsoftheeigerduncti

8、onsdboththeangularmomentumoperatorsJxac【ywhichareex—pressedbythecommoneigenstatesfJ，m)oftheangularmomen