QMGreensite_merged
195 whichhasthegeneralsolution u(ρ)=Ae−ρ/^2 +Beρ/^2 (12.14) Thesecondterm,proportionaltotheconstantB,isnon-normalizable,therefor ...
196 CHAPTER12. THEHYDROGENATOM Sincethisequationhastobetrueforeveryvalueofρ,itfollowsthatthecoefficient ofeachpowerofρmustvanish ...
197 Forthehydrogenatom,theonlywaytohaveanormalizablesolutionisifoneof thecjcoefficientsvanishes,i.e. forsomej=js,wehavecjs+1=0. ...
198 CHAPTER12. THEHYDROGENATOM Fnl(ρ) = n−∑l− 1 j=0 cjρj cj+1 = j+l+ 1 −λ (j+1)(j+ 2 l+2) cj c 0 = 1 (12.36) withthenormalizatio ...
199 Inatomicphysics,theintegervaluesofthelquantumnumberareassignedletters, namely: l = 0 S l = 1 P l = 2 D l = 3 F (12.43) Beyon ...
200 CHAPTER12. THEHYDROGENATOM WemustnormalizethewavefunctiontodetermineN: 1 = ∫ r^2 drdΩ|φ 100 |^2 = N^2 ∫ drr^2 u 10 (2r/a 0 ) ...
12.1. THESCALEOFTHEWORLD 201 normalizationgivesN=(2a 0 )−^1 /^2 ,andtherefore φ 200 = 1 √ 8 πa^30 ( 1 − r 2 a 0 ) e−r/^2 a^0 (12 ...
202 CHAPTER12. THEHYDROGENATOM becausethevolumeofasoliddependsmainlyonthenumberofatoms,andthesize ofeachatom. Theenergyreleasedi ...
12.1. THESCALEOFTHEWORLD 203 Toestimatetheenergyreleasedbyburningamoleofanything,assumethatthe energyreleasedpermoleculeisoftheo ...
204 CHAPTER12. THEHYDROGENATOM ...
Chapter 13 Electron Spin Letsgoback,foramoment,totheclassicalpictureoftheHydrogenatom,withan electronmovinginacircularorbitaroun ...
206 CHAPTER13. ELECTRONSPIN whereH 0 istheHydrogenatomHamiltonianintheabsenceofanexternalfield H 0 = p^2 2 M − e^2 r (13.6) Goin ...
207 wheregissomeconstant,knownasthegyromagneticratio. InquantumtheoryS mustbeaHermitianoperator,andweassumethatitsatisfiesthesam ...
208 CHAPTER13. ELECTRONSPIN sothez-componentoftheforceis Fz = ∂Bz ∂z μz = eg 2 Mc ∂Bz ∂z Sz (13.20) Ameasurementof the deflectio ...
13.1. SPINWAVEFUNCTIONS 209 pictureisinadequate,andinanycasetherearenosphericalharmonicswiths=^12. So...whattodo? Forthemomentle ...
210 CHAPTER13. ELECTRONSPIN Thisisthecolumnvectorrepresentationofthevector%v,inthebasis{%e 1 , %e 2 }. You willnoticethatthecomp ...
13.1. SPINWAVEFUNCTIONS 211 Incolumnvectornotation,thisiswritten [ v′ 1 v′ 2 ] = [ M 11 M 12 M 21 M 22 ][ v 1 v 2 ] (13.38) Afte ...
212 CHAPTER13. ELECTRONSPIN = < 1 2 1 2 |Sx| 1 2 − 1 2 > = 1 2 [ < 1 2 1 2 |S+| 1 2 − 1 2 >+< 1 2 1 2 |S−| 1 2 − ...
13.1. SPINWAVEFUNCTIONS 213 and,inaddition, Szψ= 1 2 ̄hψ (13.49) whereSzisthematrixshownin(13.45).Itseasytoseethatthesolutionis ...
214 CHAPTER13. ELECTRONSPIN where”spinup”and”spindown”refertothetwopossibilitiesoffindingsz=^12 and sz=−^12 .Comparingthelasttwo ...
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