亥姆霍茲微分方程——極座標

1/rpartial/(partialr)(r(partialF)/(partialr))+1/(r^2)(partial^2F)/(partialtheta^2)+k^2F=0.

F(r,theta)=R(r)Theta(theta),

(d^2R)/(dr^2)Theta+1/r(dR)/(dr)Theta+1/(r^2)(d^2Theta)/(dtheta^2)R+k^2RTheta=0.

((r^2)/R(d^2R)/(dr^2)+r/R(dR)/(dr)+k^2r^2)+(1/Theta(d^2Theta)/(dtheta^2))=0.

(d^2Theta)/(dtheta^2)1/Theta=-m^2,

Theta(theta)=A_mcos(mtheta)+B_msin(mtheta).

((r^2)/R(d^2R)/(dr^2)+r/R(dR)/(dr)+k^2r^2)=m^2.

R(r)=C_mJ_m(kr)+D_mY_m(kr),