Green Functions for Time- Dependent Problems 标准的做法是:考虑到方程是一个非齐次方程, 所以将Gren函数按相应齐次问题本征函数展开 采用平面极坐标系,坐标原点放在圆心 G(r;r=Ro(r) IRmi(r)cos mo+Rm2(r)sin mo] 6(x-)=-06(7-7) 12丌丌 >Icos mo cos mo+sin mo sin mo' m=
Green Function of Helmholtz Eq ... Green Functions for Time-Dependent Problems Separation of Variables Method of Images IO{´µÄ§´àg§§ ¤±òGreen¼êUAàg¯K ¼êÐm æ^²¡4IX§I:3 % G(r; r 0 ) =R0(r) + X ∞ m=1 Rm1(r) cos mφ+Rm2(r) sin mφ δ(r−r 0 ) = 1 r 0 δ(r − r 0 ) × 1 2π + 1 π X ∞ m=1 cos mφ cos mφ0+sin mφ sin mφ0 C. S. Wu 18ù Green¼ê()
决定R0(r)的常微分方程定解问题 1d「dRo(r) 11 r dr d 2n0 R0(0)有界Fo(a)=0
Green Function of Helmholtz Eq ... Green Functions for Time-Dependent Problems Separation of Variables Method of Images û½R0(r)~©§½)¯K 1 r d dr r dR0(r) dr = − 1 2πε0 1 r 0 δ(r − r 0 ) R0(0)k. R0(a) = 0 R0(r) = ( A0, r < r0 , B0 ln r a , r > r0 C. S. Wu 18ù Green¼ê()
决定R0(r)的常微分方程定解问题 1d「dRo(r) 11 r dr d R0(0)有界Fo(a)=0 (r) Bo In
Green Function of Helmholtz Eq ... Green Functions for Time-Dependent Problems Separation of Variables Method of Images û½R0(r)~©§½)¯K 1 r d dr r dR0(r) dr = − 1 2πε0 1 r 0 δ(r − r 0 ) R0(0)k. R0(a) = 0 R0(r) = ( A0, r < r0 , B0 ln r a , r > r0 C. S. Wu 18ù Green¼ê()
决定R0(r)的常微分方程定解问题 1d「dRo(r) 11 d d R0(0)有界 (r) T Bo In r2+0 dro(r) r+0 11 27Eo r
Green Function of Helmholtz Eq ... Green Functions for Time-Dependent Problems Separation of Variables Method of Images û½R0(r)~©§½)¯K 1 r d dr r dR0(r) dr = − 1 2πε0 1 r 0 δ(r − r 0 ) R0(0)k. R0(a) = 0 R0(r) = ( A0, r < r0 , B0 ln r a , r > r0 R0(r) r 0+0 r 0−0 = 0 dR0(r) dr r 0+0 r 0−0 = − 1 2πε0 1 r 0 C. S. Wu 18ù Green¼ê()
决定R0(r)的常微分方程定解问题 1d「dRo(r) 11 r dr d R0(0)有界Fo(a)=0 Ro(r) Bo In 1 Ao=tEO a n
Green Function of Helmholtz Eq ... Green Functions for Time-Dependent Problems Separation of Variables Method of Images û½R0(r)~©§½)¯K 1 r d dr r dR0(r) dr = − 1 2πε0 1 r 0 δ(r − r 0 ) R0(0)k. R0(a) = 0 R0(r) = ( A0, r < r0 , B0 ln r a , r > r0 A0 = − 1 2πε0 ln r 0 a B0 = − 1 2πε0 C. S. Wu 18ù Green¼ê()