决定Rm2()的常微分方程定解问题 1 dd rm2(r) 6(r-r) sin mo lEOr Rm2(0)有界R2m2(a)=0 n2 B 1 rr\n sin mo r<rl Rm2(7)= 1 sin mq 2丌0m
Green Function of Helmholtz Eq ... Green Functions for Time-Dependent Problems Separation of Variables Method of Images û½Rm2(r)~©§½)¯K h 1 r d dr r d dr − m2 r 2 i Rm2(r) = − δ(r − r 0 ) πε0r 0 sin mφ0 Rm2(0)k. Rm2(a) = 0 Rm2(r) = ( Am2 r a m r < r0 Bm2 hr a m − a r mi r > r0 Rm2(r) = (− 1 2πε0 1 m hrr0 a 2 m − r r 0 mi sin mφ0 r < r0 − 1 2πε0 1 m hrr0 a 2 m − r 0 r mi sin mφ0 r > r0 C. S. Wu 18ù Green¼ê()
圆内 Poisson方程第一边值问题Gren函数 V2G(r;r)=--6(r-r)r<a,|r1<a G(r;r)==0
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 r < r0 G(r; r 0 )=− 1 2πε0 ln r 0 a + X∞ m=1 1 m hrr0 a 2 m − r r 0 mi cos m(φ−φ 0 ) r > r0 G(r; r 0 )=− 1 2πε0 ln r a + X∞ m=1 1 m hrr0 a 2 m − r 0 r mi cos m(φ−φ 0 ) C. S. Wu 18ù Green¼ê()
圆内 Poisson方程第一边值问题Gren函数 V2G(r;r)=--6(r-r)r<a,|r1<a G(r;r)==0 当r<'时 G( n 2πeo cosm(o-o)
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 r < r0 G(r; r 0 )=− 1 2πε0 ln r 0 a + X∞ m=1 1 m hrr0 a 2 m − r r 0 mi cos m(φ−φ 0 ) r > r0 G(r; r 0 )=− 1 2πε0 ln r a + X∞ m=1 1 m hrr0 a 2 m − r 0 r mi cos m(φ−φ 0 ) C. S. Wu 18ù Green¼ê()
圆内 Poisson方程第一边值问题Gren函数 V2G(r;r)=--6(r-r)r<a,|r1<a G(r;r)==0 当r<'时 G( n 2πeo cosm(o-o) 当r>r时 G(r;r)=-1 ml(a2 cosm(0一d 2T0
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 r < r0 G(r; r 0 )=− 1 2πε0 ln r 0 a + X∞ m=1 1 m hrr0 a 2 m − r r 0 mi cos m(φ−φ 0 ) r > r0 G(r; r 0 )=− 1 2πε0 ln r a + X∞ m=1 1 m hrr0 a 2 m − r 0 r mi cos m(φ−φ 0 ) C. S. Wu 18ù Green¼ê()
Green Functions for Time- Dependent Problems 评述 这种方法,将Gren函数按相应齐次问题的本 征函数展开,一般说来,得到的解式会是无 穷级数 当然,不排除在某些特殊情形下可以将级数 例如,现在得到的解式就是如
Green Function of Helmholtz Eq ... Green Functions for Time-Dependent Problems Separation of Variables Method of Images µã ù«{§òGreen¼êUAàg¯K ¼êÐm§`5§)ª¬´Ã ¡?ê ,§ØüØ3, AÏ/e±ò?ê ¦Ú ~X§y3)ªÒ´Xd ØL§ùI'ÙG?ê¦ÚE| C. S. Wu 18ù Green¼ê()