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8. (Fourier transformation and Dirac delta-function) Use Fourier transform to solve Poisson's equation for a point charge V2 = −4лd(†) in 3-dimensions. Useful tips: ƒſſ‰ƒ(†)8(r)d³ř = f(0), [[[°¸ d³ř = [² do [¹, dcose (r² dr, and 0⁰: moo sinx -2πT dx = "

8. (Fourier transformation and Dirac delta-function) Use Fourier transform to solve Poisson's equation for a point charge V2 = −4лd(†) in 3-dimensions. Useful tips: ƒſſ‰ƒ(†)8(r)d³ř = f(0), [[[°¸ d³ř = [² do [¹, dcose (r² dr, and 0⁰: moo sinx -2πT dx = "

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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