(Fourier transformation and Dirac delta-function) Use Fourier transform to solve Poisson's equation for a point charge V²¢ = −4n8(7) in 3-dimensions. Useful tips: ¶ſſ‰ƒ(7)8(7)d³7 = ƒ(0), ƒſſ‰d³† = f²″ d¢ ſ¹dcose fºr² dr, and f co sinx dx = 7/1/1 x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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8.
(Fourier transformation and Dirac delta-function) Use Fourier transform to solve Poisson's
3-dimensions. Useful tips:
equation for a point charge V² = −4nd(r) in
-4πδ
∞
·2π
oo sinx
ƒſſ‰ƒ (†)8(†)d³7 = ƒ(0), ƒſſ‰d³† = ƒ²¹ dø ƒ¹₁ dcose ſºr² dr, and ſ dx
-1
X
-
T
2
■
Transcribed Image Text:8. (Fourier transformation and Dirac delta-function) Use Fourier transform to solve Poisson's 3-dimensions. Useful tips: equation for a point charge V² = −4nd(r) in -4πδ ∞ ·2π oo sinx ƒſſ‰ƒ (†)8(†)d³7 = ƒ(0), ƒſſ‰d³† = ƒ²¹ dø ƒ¹₁ dcose ſºr² dr, and ſ dx -1 X - T 2 ■
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