6.1 6.2 and 6.6

6.1 6.2 and 6.6 - PhysicsH7CFall1999 SolutionstoProblemSet7...

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Unformatted text preview: PhysicsH7CFall1999 SolutionstoProblemSet7 DerekKimball AbovethefrontdoorofNielsBohrscottagewasnailedahorseshoe.Avisitorwho sawitexclaimed:Beingasgreatascientistasyouare,doyoureallybelievethat ahorseshoeabovetheentrancetoahomebringsgoodluck? No,answeredBohr,Icertainlydonotbelieveinthissuperstition.Butyou know,headdedwithasmile,theysaythatitdoesbringluckevenifyoudont believeinit!-GeorgeGamow,excerptedfrom ThirtyYearsthatShookPhysics . Ifyouhaveanyquestions,suggestionsorcorrectionstothesolutions,donthesitate toe-mailmeatdfk@uclink4.berkeley.edu! Problem1 Thisproblemmakessenseonlyifyoumakesomeratherpoorlymotivatedap- proximations.Inparticular,wemustassumethatwearefarawayfromresonance (namelythat 2 2 ).Wealsocanassumethatthereareveryfewelectrons (namelythat Ne 2 m 1,whichiswell-motivatedbythefactthat ismuchlessthan n ,i.e.fewabsorbers).Ifwemaketheseapproximations,theresultsfollowalmost immediately.Ifyoudontmaketheseassumptions,thentheresultsareclearly incorrect(seeFigure6.1inFowles,whichisnothingliketheequationsFowlesasks ustoderive).Thus,wellmaketheseassumptions! Thenwecanapplytheseapproximationstoequations6.34and6.35inFowles.We findthat: n 2 2 n 2 1+ Ne 2 m 1 2 2 (1) UsingafirstorderTaylorexpansion,wethenfindthat:...
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6.1 6.2 and 6.6 - PhysicsH7CFall1999 SolutionstoProblemSet7...

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