kim,group theoretical methods and applications to molecules and crystals

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1、ThispageintentionallyleftblankThisbookexplainsthebasicaspectsofsymmetrygroupsasappliedtoproblemsinphysicsandchemistryusinganapproachpioneeredanddevelopedbytheauthor.Thesymmetrygroupsandtheirrepresentationsareworkedoutexplicitly,eliminatingtheundulyabstractnatur

2、eofgrouptheoreticalmethods.TheauthorhassystematizedthewealthofknowledgeonsymmetrygroupsthathasaccumulatedduringthecenturysinceFedrovdiscoveredthe230spacegroups.Allspacegroups,unitaryaswellasanti-unitary,arereconstructedfromthealgebraicde®ningrelationsofthepoint

3、groups.Thematrixrepresentationsaredeterminedthroughtheprojectiverepresentationsofthepointgroups.Therepresentationsofthepointgroupsaresubducedbytherepresentationsoftherotationgroup.Thecorrespondencetheoremonbasisfunctionsbelongingtoarepresentationisintroducedtof

4、ormthegeneralexpressionforthesymmetry-adaptedlinearcombinationsofequivalentbasisfunctionswithrespecttoapointgroup.Thisisthenappliedtoformmolecularorbitalsandsymmetrycoordinatesofvibrationofamoleculeoracrystalandtheenergybandeigenfunctionsoftheelectronsinacrysta

5、l.Thebookassumesonlyanelementaryknowledgeofquantummechanics.Numerousapplicationsofthetheoremsaredescribedtoaidunderstanding.Thisworkwillbeofgreatinteresttograduatestudentsandprofessionalsinsolidstatephysics,chemistry,mathematicsandgeologyandtothosewhoareinteres

6、tedinmagneticcrystalstructures.To`Eomma'GroupTheoreticalMethodsandApplicationstoMoleculesandCrystalsSHOONK.KIMTempleUniversityThePittBuilding,TrumpingtonStreet,Cambridge,UnitedKingdom

7、TheEdinburghBuilding,CambridgeCB22RU,UK40West20thStreet,NewYork,NY10011-4211,USA477WilliamstownRoad,PortMelbourne,VIC3207,AustraliaRuizdeAlarcón13,28014Madrid,SpainDockHouse,TheWaterfront,CapeTown8001,SouthAfricahttp://www.cambridge.org©ShoonKKim2004Firstpublis

8、hedinprintedformat1999ISBN0-511-03620-5eBook(AdobeReader)ISBN0-521-64062-8hardbackContentsPrefacepagexvListofsymbolsxvii1Lineartransformations1.1Vectors11.2Lineartransformat