Explicitcalculationshowsthatthezeroorderofquantummechanicalmatrixelementsofhydrogenatom’sinverseradiusinthequasi classicalcaseareHeisenbergmatrixelements,andthefirst ordertermplaysarolewhenthedifferencebetweentheprincipalquantumnumbersislarge .Intheclassicallimit,quantummechanicalresultsareidenticaltoHeisenbergones
Explicitcalculationshowsthatthezeroorderofquantummechanicalmatrixelementsofhydrogenatom’sinverseradiusinthequasi classicalcaseareHeisenbergmatrixelements,andthefirst ordertermplaysarolewhenthedifferencebetweentheprincipalquantumnumbersislarge .Intheclassicallimit,quantummechanicalresultsareidenticaltoHeisenbergones
Thesurfaceroughnessdependenceoftheopticalfieldatuocorrelationfunctionandtheintensityautocorrelationfunctionofthespecklepattern ,producedinthefarfieldundertheilluminationofaGaussianbeam ,hasbeentheoreticallyinvestigatedwiththeassumptionthattheirregularitiesofthetargetsurfacesarelargerthanthelaserwavelength.Analyticalexpressionsforthefirst andsecond ordermomentsoftheintensityhavebeenderived,andthesizeofthespecklecellhasbeencomputed.Theanalysisindicatesthatthemeanintensityofthespecklepatternsiscloselyrelatedtotheratioofthelateralcorrelationlengthtothesurfaceroot mean squareheightofthesurface.Whereasthesizeofthespecklecellandthecorrelationdegreeofthespeckleintensitiesareshowntobeindependentoftheparameterscharacterizingtheroughnessofasurface,andonlydeterminedbythela serbeamwaist.
Thesurfaceroughnessdependenceoftheopticalfieldatuocorrelationfunctionandtheintensityautocorrelationfunctionofthespecklepattern ,producedinthefarfieldundertheilluminationofaGaussianbeam ,hasbeentheoreticallyinvestigatedwiththeassumptionthattheirregularitiesofthetargetsurfacesarelargerthanthelaserwavelength.Analyticalexpressionsforthefirst andsecond ordermomentsoftheintensityhavebeenderived,andthesizeofthespecklecellhasbeencomputed.Theanalysisindicatesthatthemeanintensityofthespecklepatternsiscloselyrelatedtotheratioofthelateralcorrelationlengthtothesurfaceroot mean squareheightofthesurface.Whereasthesizeofthespecklecellandthecorrelationdegreeofthespeckleintensitiesareshowntobeindependentoftheparameterscharacterizingtheroughnessofasurface,andonlydeterminedbythela serbeamwaist.
WehavemeasuredthetransformationtemperatureofNi52 . 2 Mn2 3 . 8Ga2 4singlecrystallinesamplebyvariousmethods,suchasDSC ,magnetization ,acmagneticsusceptibility,dcresistance,andtransformationstrain .Comparingtheexperimentalresultsbetweeneachother,wefoundthat,duetothedifferentphysicalmechanism ,variousmeasuringmethodswillgivedifferentmar tensitictransformationtemperatures.Basedontheseobservations,wesuggestamulti steplatticedeformationforthetransforma tionofNiMnGa,whichissimilartotheG Trelation .ThewholeprocessoftransformationcanbeobservedbyDSCandR Tmea surements ,whilethemagneticmeasurementsisonlysensitivetotheformationofmartensiticlattices.Themeasurementontrans formationstrainisnotsoreliableforthetransformationtemperatureastheothermeasurements,butitreallyreflectsthesituationofthesub structures,suchastwinboundaries,variantsanddefectsinthematerial.
WehavemeasuredthetransformationtemperatureofNi52 . 2 Mn2 3 . 8Ga2 4singlecrystallinesamplebyvariousmethods,suchasDSC ,magnetization ,acmagneticsusceptibility,dcresistance,andtransformationstrain .Comparingtheexperimentalresultsbetweeneachother,wefoundthat,duetothedifferentphysicalmechanism ,variousmeasuringmethodswillgivedifferentmar tensitictransformationtemperatures.Basedontheseobservations,wesuggestamulti steplatticedeformationforthetransforma tionofNiMnGa,whichissimilartotheG Trelation .ThewholeprocessoftransformationcanbeobservedbyDSCandR Tmea surements ,whilethemagneticmeasurementsisonlysensitivetotheformationofmartensiticlattices.Themeasurementontrans formationstrainisnotsoreliableforthetransformationtemperatureastheothermeasurements,butitreallyreflectsthesituationofthesub structures,suchastwinboundaries,variantsanddefectsinthematerial.