complex function Φn=Aemo (m=0,±1，±2，…） Usually,real functions are used,which are deduced from the complex function according to the assumption of the linear combination of these states Aeo=Acosmo+iAsinmo -m=Ae mo=Acosmo-iAsin mo ④D1=Φm+①-m=2Ac0smp=Bcosmp Φ2=Φm-Φm=2 iAsin mo=B'sinmo m normalization condition 1 (2 (Bcosmo)2dΦ=B2π=1 Φ Jo ΦΦdΦ= cosmo B sinmo Table The solution ofΦ（φ）equation m complex form real form 1 1 0 Φ0=1 2元 D022r 1 ①1= cos √2π Vπ 1 Φ1= e ip Φ= 1 sin √2元 Vπ 1 1 2 Φ2= cos20 √2π Φ= Vπ -2= Φ -sin 20 √2π Vπϕ ϕ ϕ ϕ iA m B m A m B m m m m m 2 sin 'sin 2 cos cos 2 1 Φ = Φ − Φ = = Φ = Φ + Φ = = − − Usually, real functions are used, which are deduced from the complex function according to the assumption of the linear combination of these states . complex function Φ = Ae (m = 0,±1,±2,⋅⋅⋅⋅⋅⋅) im m ϕ ϕ ϕ ϕ ϕ ϕ ϕ Ae A m iA m Ae A m iA m im m im m cos sin cos sin Φ = = − Φ = = + − − π ϕ π π π 1 ( cos ) 1 2 2 2 0 1 * 1 2 0 = Φ Φ Φ = Φ = = ∫ ∫ B d B m d B normalization condition ϕ π ϕ π m m sin 1 cos 1 2 1 Φ = Φ = Table The solution of Φ(φ) equation ϕ π π ϕ π π ϕ π π ϕ π π π π ϕ ϕ ϕ ϕ sin 2 1 2 1 2 cos 2 1 2 1 2 sin 1 2 1 1 cos 1 2 1 1 2 1 2 1 0 sin 2 2 2 cos 2 2 2 sin 1 1 cos 1 1 0 0 − Φ = Φ = Φ = Φ = − Φ = Φ = Φ = Φ = Φ = Φ = ± − − ± ± − − ± i i i i e e e e m complex form real form