Re: [問題] 請教 Green's Function 用在 PDE 的概念？
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δG
∫ u(r1)．——(r,r1)．dS(r1)
S δn
^
= ∫ u(r1)．[ ▽G(r,r1)．n ]．dS(r1)
S
δG (r,r1) ^ ^
= ∫ u(r1)．[ —————— (r-r1)．n ]．dS(r1)
S δ(r-r1)
1 ^ ^
= ∫ u(r1)．[ —————— (r-r1)．n ]．dS(r1)
S 4π(r-r1)^2
--------------------------------------------------
→
The electrostatic potential at position r
due to an electric dipole at the origin is given by:
→ ^
1 p．r
u = ————．———
4πε r^2
--------------------------------------------------
^ ^
1 u(r1) n．(r-r1)
= ∫ [ ——————．———————— ]．dS(r1)
S 4π (r-r1)^2
note: 經過一連串的轉換, boundary conditions 的效應被擬人化了
實際上 boundary conditions 可能不是 dipole 造成的, 但我
們很自high的把他看作是邊界上的等效dipole造成的位能。
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◆ From: 218.162.225.112
※ 編輯: LeeSeDol 來自: 218.162.225.112 (01/30 01:49)
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