資源描述：
《teoria de grupos symmetry, structure spectroscopy group theory外語(yǔ)英文電子書(shū)》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在教育資源-天天文庫(kù)。
1、Chemistry239Symmetry,StructureandSpectroscopy:GroupTheoryanditsApplicationsPeterR.TaylorSanDiegoSupercomputerCenterandDepartmentofChemistryandBiochemistryUniversityofCalifornia,SanDiegotaylor@sdsc.eduhttp://www.sdsc.edu/~taylorSanDiegoSupercomputerCenterChemistry239Abs
2、tractGroupTheory?Considerasetofobjects{G}andaproductruledenoted?thatallowsustocombinethem.?DenotedF?G,whereF,G∈{G}.?{G}canbeobjectssuchasnumbersorvariables,oroperators.SanDiegoSupercomputerCenterChemistry239Examples?Theintegersandanyofthebinaryoperationsofarithmetic:?=
3、+:1+5=6(1)?=?:1?5=?4=5?1(2)(12?3)?7=3=12?(3?7)=16(3)?=÷:12÷3=4=3÷12(notevenaninteger)(4)?Notethatsofartherearenorequirementsthat?shouldobeycertainrules,suchascommutativityorclosure.SanDiegoSupercomputerCenterChemistry239Examples?Translationsorrotationsofaphysicalobj
4、ectintwoorthreedimensions.Here?denotessuccessivetransformations.????cosθ?sinθ0cosφ?sinφ0??????sinθcosθ0?????sinφcosφ0??001001?Thesecommute,unlike????cosθ?sinθ0cosφ0?sinφ??????sinθcosθ0?????010??001sinφ0cosφSanDiegoSupercomputerCenterChemistry239Examples?Permutationsofo
5、bjects:supposewehaveaset{ABC}andwehavepermutationsde￡nedby,e.g.,(312){ABC}={CAB}?Then(312)?(213){ABC}=(312){BAC}={CBA}SanDiegoSupercomputerCenterChemistry239Closure?RequirethatifF,G∈{G},thenF?G∈{G}andG?F∈{G}.?NotethatthisdoesnotimplyF?G=G?F.?Suchasetandclosedproductrul
6、ecompriseagruppoid.?Forexample,theintegersareclosedunderaddition,multiplication,andsubtraction,butnotunderdivision.?ThesetofpermutationsofNobjectsisclosedwithrespecttosuccessivepermutations.?SuccessiverotationsandtranslationsinMdimensionsareclosed.SanDiegoSupercomputer
7、CenterChemistry239Imposingfurtherrules?Gruppoidsareclearlyverygeneralthings.?Fewusefulpropertiesareknownforgruppoids—wehavetorestrictourselvesfurther.?Imposerestrictionsonoursetandproductrule.SanDiegoSupercomputerCenterChemistry239Associativity?RequirethatifF,G,H∈{G},w
8、ehave(F?G)?H=F?(G?H).?Forexample,theadditionandmultiplicationofintegersisassociative,whereassubtractionisnot.?Success
