05_05_02 - 167 That vector with spin(r = Anl m Rnl(r)Yl m =...

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[email protected] 167 ˆ z l s l l s L nl m s m m nl m s m = ! That vector with spin 05/02/2005 7KHUH±LV±DQ±DGGLWLRQDO±SDUDPHWHU±WKDW±WKH±VWDWHV±KDYH±WR±GHWHUPLQH²±WKH±VSLQ³ all all ( , , ) ( ) ( , ) l nl m nl l m n l m l r A R r Y ϑϕ =- Ψ = ∑∑ ∑ all all l nl m n l m l A nl m =- Ψ = ∑∑ ∑ V\PEROLF±±±±±QRWDWLRQ 1 2 1 2 all all l s l s l nl m m l s n l m l m A nl m s m =- =- Ψ = ∑∑ ∑ ∑ 7KH±EDVLV±VWDWHV±DUH±QRZ±VLPXOWDQHRXV±HLJHQIXQFWLRQV±RI² ˆ l s nl l s E nl m s m E nl m s m = 2 2 ˆ ( 1) l s l s L nl m s m l l nl m s m = + ! 2 2 3 4 ˆ l s l s S nl m s m nl m s m = ! ˆ z l s s l s S nl m s m m nl m s m = ! 1RWH±WKDW±LW±ZDV±DQ± DUELWUDU\± FKRLFH WR±KDYH±WKH±EDVLV±VWDWHV± KDYH±WKH± ODVW±´ SURSHUWLHV±VLQFH± / DQG±6 GR±QRW±FKDQJH±WKH± HQHUJ\³
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[email protected] 168 The radial part of the wave function 05/02/2005 7KH±HIIHFWLYH±UDGLDO±SRWHQWLDO² 2 2 2 2 2 2 0 ( 1) 1 1 1 4 2 2 [ ] ( ) l l e
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05_05_02 - 167 That vector with spin(r = Anl m Rnl(r)Yl m =...

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