Ym(0, p)=NmP(cos 0)e (19 m (8, p)m(0, sin eded = n 20) (20)缔结 legendre函数正交性: 2TNIm o ml pIm sin dedo=du pIm 而球谐函数 r Yn(e,Q)Ym(e, ) sin dedo (21) 4氢原子波函数,算符: h210(20)12 H 2r2ar、a)2（20）缔结legendre函数正交性： 而球谐函数： 4.氢原子波函数，算符： ( , cos (19) ) ( ) m im Y N P e lm lm l     = ( ) ( ) 2 0 0 , , sin (20) lm l m ll Y Y d d              =   2 sin m m      N N P P d d lm l m l l ll    =  ( ) ( ) 2 0 0 , , sin (21) lm l m ll mm Y Y d d                 =   2 2 2 2 2 2 2 2 2 1 2 2 2 s s e e l H r   r r r r r r      = −  − = − + −      