let hod 圆内 Poisson方程第一边值问题Gren函数 V2G(r;r)=-6(r-r)r<a,|r1<a 0 G(r;r) 0 T=a 其中 72=2+y2V3=2202 ax2 ay2
Green Function of Helmholtz Eq ... Green Functions for Time-Dependent Problems Separation of Variables Method of Images SPoisson§1>¯KGreen¼ê ∇2 2G(r; r 0 ) = − 1 ε0 δ(r − r 0 ) |r| < a, |r 0 | < a G(r; r 0 ) r=a = 0 Ù¥ r 2 = x 2 + y 2 ∇2 2 = ∂ 2 ∂x2 + ∂ 2 ∂y2 C. S. Wu 18ù Green¼ê()
讲授要点 ③圆内 Poisson方程第一边值问题的 Green函数 分离变量法 电像法 0含时问题的 creen函数 。提法:定解问题 对称性 。含时问题的 Green函数解法 Green函数的求法
Green Function of Helmholtz Eq ... Green Functions for Time-Dependent Problems Separation of Variables Method of Images ùÇ: 1 SPoisson§1>¯KGreen¼ê ©lCþ{ >{ 2 ¹¯KGreen¼ê J{µ½)¯K é¡5 ¹¯KGreen¼ê){ Green¼ê¦{ C. S. Wu 18ù Green¼ê()
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 Creen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
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()
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 Rmi(r) cosmo+Rm2()sin mo
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()
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] cos moos mosin mosin no
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()