60 CHAPTER 3. œPõfü⌃ 3.10 õfœó&Ñq,Å˝p %<ÑÙ⌘ÏÂSõfœÑ^é,Å<Ñ,Å‚/c§RÑ⇥F/⌘Ïv°‘∆vÄv(*,Å<$*Â⌦,Å‚)≈µ⇥Çú˙∞ÄvH›¡,Å‚c§b)($*⇢*õfœÑq,Å˝p⌘ÏÔ„≥Äv&eÑÓò⇥ Gæ ˆ Aˆ B/$*õfœÑó&. X(ÕÔ˝: ÉÏwqÑ,Å˝p ˆ A|nl i = a n |nl i, ˆ B|nl i = b l |nl i. (3.219) |nl i\ ˆ A, ˆ BÑq,Å. ÇúíP⌅éŸ7Ñ∂, KœAóa n , KœBób l . KœKÑ∂ÿ. HK K‡@◆. ( ˆ A ˆ B - ˆ B ˆ A)|nl i =(a n b l - b l a n )|nl i =0. (3.220) Ë✏: ˆ A, ˆ B ˘◆/(⌦✏˘˚✏‚˝p˝⇣ÀÑ≈µ↵. Ÿ≥ÂÙ÷Ï˘◆F/Ÿ✏s@ ˆ Aˆ B àÔ˝ /˘◆Ñ. Ÿ/Ô¡ÑM–/|nl iÑ⇣å⌥˝p˚, ˚U˝ÔÂ(ÉU|i = X nl C nl |nl i, (3.221) é/ ( ˆ A ˆ B - ˆ B ˆ A)|i = X nl C nl ( ˆ A ˆ B - ˆ B ˆ A)|nl i = X nl C nl (a n b l - b l a n )|n li =0. (3.222) ‡d,[ ˆ A, ˆ B] = 0. Õ«e, ⌘ÏÔ¡: ÇúÑ∆ó& ˆ A, ˆ B ˘◆, ⇡ÉÏ≈öX(˚⌫q,Å˝p. ¡: Gæ|n i,n =1, 2, ··· ,|Φ l i,l =1, 2, ··· ,⌃+/ó& ˆ A, ˆ Bу,Å, 1éA, B ˝/õfœ@Ÿ$ƒ,Å⌅Í˝/å⌥Ñ. ˆ A|n i = a n |n i,n =1, 2, 3, ··· , ˆ B|Φ l i = b l |Φ l i,l =1, 2, 3, ··· . (3.223) ⇤Q0Ô˝ÑÄv, ⌘Ï⌃|Φ l i,Å<⌃ƒ(b i 6= b j , Çúi 6= j ) ˆ B|Φ i⌫ i = b i |Φ i⌫ i,i =1, 2, 3, ··· ; ⌫ =1, ··· ,f i . (3.224) f i 1/b i ÑÄv¶⇥ ˚✏÷* ˆ AÑ,Å˝p|n i, U⇣|Φ i⌫ iч† |n i = X i⌫ c (n) i⌫ |Φ i⌫ i = X i | ˜ Φ ni i (3.225) v-| ˜ Φ ni i = P ⌫ c (n) i⌫ |Φ i⌫ i, Õ6/ ˆ BÑ,Å˝p, ^é,Å<b i . ⇤Q ( ˆ A - a n )|n i = X i ( ˆ A - a n )| ˜ Φ ni i =0. (3.226) 1é ˆ Aˆ B˘◆, ⌘ψ B( ˆ A - a n )| ˜ Φ ni i =( ˆ A - a n ) ˆ B| ˜ Φ ni i = b i ( ˆ A - a n )| ˜ Φ ni i. (3.227) Çú( ˆ A - a n )| ˜ Φ ni i:ˆ, É1/ ˆ BÑ,Å, ^é,Å<b i . F/(3.226)hŸõ/ø'¯sÑ. * Ñ∆ó&Ñ^é,Å<Ñ,Å˝p/c§Ñ, Ô˝ø'¯s. @ ( ˆ A - a n )| ˜ Φ ni i =0. (3.228)
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60 CHAPTER 3. œPõfü⌃
3.10 õõõfffœœœóóó&&&ÑÑÑqqq���,,,ÅÅÅ˝ppp
%<ÑÙ�⌘ÏÂSõfœÑ^é��,Å<Ñ,Å‚/c§R�Ñ⇥F/⌘Ïv° ‘∆vÄv(��
*,Å< $*Â⌦,Å‚)≈µ⇥Çú˙∞Äv��H›¡,Å‚c§b�)($*�⇢*õfœÑq�
,Å˝p�⌘ÏÔ„≥Äv&eÑÓò⇥
GæA�B/$*õfœÑó&. X(�ÕÔ˝: ÉÏw q�Ñ,Å˝p
A| nli = an| nli, B| nli = bl| nli. (3.219)
| nli\A, BÑq�,Å�. ÇúíP⌅éŸ7Ñ∂�, KœAóan, KœBóbl. KœK�Ñ∂��ÿ. HK
�K‡@◆.
(AB � BA)| nli = (anbl � blan)| nli = 0. (3.220)
ËËË✏✏✏: A, B˘◆◆◆///(((⌦⌦⌦✏✏✏˘˚✏✏✏‚‚‚˝ppp˝⇣⇣⇣ÀÀÀÑÑÑ≈≈≈µµµ↵↵↵. Ÿ�≥ÂÙ÷Ï˘◆�F/Ÿ✏s@A�BàààÔÔÔ˝