量子力學(xué)第七章習(xí)題-免費(fèi)閱讀
【正文】 解： )]()([)]()([ 22/112/122/112/1)1()1( zzzzSS SSSS ?????? ?? ? )S()S()S()S( z22/1z12/1z12/1z22/1 ???? ??? )S()S( z22/1z22/1 ?? ?? = 1 )]()([)]()([ 22/112/122/112/1)2()1( zzzzSS SSSS ???? ? ?????? )S()S()S()S( z22/1z12/1z12/1z22/1 ????? ???? = 0 )]()()()([)]()([2122/112/122/112/122/112/1)3()1(zzzzzzSSSSSSSS???????????????? )]()()()( )()()()([2122/112/112/122/122/112/112/122/1zzzzzzzzSSSSSSSS????????????????? ]0)()([2122/122/1 ?? ??zz SS ?? = 0 同理可證其它的正交歸一關(guān)系。 設(shè)對(duì)應(yīng)于本征值2? 的本征函數(shù)為 ?????????112/1 ba? 由本征方程 2/12/1 2? ?? ??xS ，得 ?????????????????????????1111201102 baba ?? 111111 abbaab????????????????????由歸一化條件 12/12/1 ?? ?? ，得 1),(11*1*1 ?????????aaaa即 12 21 ?a ∴ 21 2111 ?? ba 對(duì)應(yīng)于本征值2? 的本征函數(shù)為 ?????????11212/1? 設(shè)對(duì)應(yīng)于本征值2?? 的本征函數(shù)為 ??????????222/1 ba? 由本征方程 ?????????? ??222/12/1 2?baS x ??? 222222 abbaab ???????????????????????由歸一化條件，得 1),(22*2*2 ??????????? aaaa 同理可求得yS?的本征值為2??。其相應(yīng)的本征函數(shù)分別為 ?????????i12121? ???????????i12121?即 12 22 ?a ∴ 21 2122 ??? ba 對(duì)應(yīng)于本征值2?? 的本征函數(shù)為 ???????????11212/1? 7 .4 求自旋角動(dòng)量)c o s,c o s,( c o
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