1 8(rOR(r)+8'm (E+e e)r2=[ 10 (sin8(0、 aΦ(p) R(r） 4πEJ (0)sine a0 a0 Φ()sin20ap2 1(r) ze- let 8πm(E+ )r2=B R(r）Or h2 Radial part,R eq. 4πE1 1 a (sin() 1 a2D() =-B Angular part ⊙(0)sin0aa a0 Φ()sin20ap2 multiplied sin20 sine (sin 1 ()=-Bsin20 ⊙(0)a 60 Φ()ab2 sine o (sin() +Bsin20=- 1 aΦ() ⊙()a8 a0 ()ap2 sin0 let (sin() +Bsin20=m2 Θ(0)a a0 p©eq. 1 ∂Φ() 三-ml DΦ Φ()a2 eq. a.Φ(b)equation d2Φ(p) dd +m2Φ()=0 Its complex form: Φ=Aetilml№，letm=±ml,Φ=Aem Normalization 2 ΦΦdΦ-=4eme地=l 1 A= V2π 1 m -cosm+- -sin mo V2元 √2 2 Φm(φ)=Φm(p+2π The values of m must be eim(+2r）=eimp.em2r m=0,±1，±2， =1 m magnetic quantum cos2mπ+isin2mn=1 numberβ πε π + + = ∂ ∂ ∂ ∂ 2 0 2 2 2 2 ) 4 ( 8 ) ( ) ( ( ) 1 r r ze E h m r R r r R r r let e ] ( ) ( )sin 1 ) ( ) (sin ( )sin 1 ) [ 4 ( 8 ) ( ) ( ( ) 1 2 2 2 2 0 2 2 2 2 φ φ θ φ θ θ θ πε θ θ θ π ∂ ∂ Φ Φ + ∂ ∂Θ ∂ ∂ Θ + + = − ∂ ∂ ∂ ∂ r r ze E h m r R r r R r r e f Angular part f Radial part, R eq. β φ φ θ φ θ θ θ θ θ θ = − ∂ ∂ Φ Φ + ∂ ∂Θ ∂ ∂ Θ 2 2 2 ( ) ( )sin 1 ) ( ) (sin ( )sin 1 β θ φ φ θ φ θ θ θ θ θ θ 2 2 2 2 sin ( ) ( ) 1 ) ( ) (sin ( ) sin sin = − ∂ ∂ Φ Φ + ∂ ∂Θ ∂ ∂ Θ multiplied 2 2 2 ( ) ( ) 1 ) sin ( ) (sin ( ) sin φ φ φ β θ θ θ θ θ θ θ ∂ ∂ Φ Φ + = − ∂ ∂Θ ∂ ∂ Θ 2 2 ) sin ( ) (sin ( ) sin let + = m ∂ ∂Θ ∂ ∂ Θ β θ θ θ θ θ θ θ 2 2 2 ( ) ( ) 1 = −m ∂ ∂ Φ Φ φ φ φ fΘ eq. fΦ eq. a. Φ(φ) equation Its complex form: Φ =Ae±i|m|φ , let m= ±|m|, Φ =Aeim φ ( ) 0 ( ) 2 2 2 + Φ = Φ φ φ φ m d d 1 2 2 0 2 0 * Φ Φ Φ = Φ = − ∫ ∫ d A e e d Normalization im im m m φ φ π π Φ (φ) = Φ (φ + 2π ) m m The values of m must be m = 0,±1,±2,⋅⋅⋅⋅⋅⋅ m : magnetic quantum number 2π 1 A = φ π φ π π φ m i e m im m sin 2 cos 2 1 2 1 Φ = = + imφ im(φ 2π ) imφ im2π e = e = e ⋅e + cos 2 sin 2 1 1 2 + = = π π π m i m eim