Re: [微積] delta function
※ 引述《ed78617 (雞爪)》之銘言:
: → →
: δ(r - r') = δ(x-x')δ(y-y')δ(z-z')
: =(1/r)δ(r-r')δ(θ-θ')δ(z-z')
: 我想問的是,柱坐標的這一式怎麼來的?
: 看起來是因為對三維空間積分時,rdrdθdz 正好可以消去(1/r)
: 那...有沒有嚴謹一點的推導方法呢
δ function is meaningful only when it is integrated with a function
∫_M f(x,y)δ(x-x')δ(y-y') dx dy = f(x',y') when M includes (x',y')
= 0 otherwise
∫_M f(r cosθ, r sinθ)δ(r-r')δ(θ-θ') r dr dθ
= r' f(r'cosθ',r'sinθ') when M includes (x',y')
= 0 otherwise
Hence, δ(x-x')δ(y-y')
=(1/r') δ(r-r')δ(θ-θ')
=(1/r) δ(r-r')δ(θ-θ')
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◆ From: 112.104.142.91
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05/29 20:06, , 1F
05/29 20:06, 1F
※ 編輯: JohnMash 來自: 112.104.142.91 (05/29 20:18)
推
05/30 11:03, , 2F
05/30 11:03, 2F
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