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Use the Fourier transform method to solve this PDE a2p(x, y, z) 220(x, y, z) 226(x, y, z) +*+$(x, y, z) Әr2 ду? az2 = 8(
Posted: Thu May 12, 2022 7:51 am
by answerhappygod
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Use the Fourier transform method to solve this PDE a2p(x, y, z) 220(x, y, z) 226(x, y, z) +*+$(x, y, z) Әr2 ду? az2 = 8(x)/(y)/(z) where k is constant and 8(x) is the Dirac delta function. The solution $(x, y, z) vanishes sufficiently fast at Foo. a) Find the solution in the Fourier space ölke, ky, kz). b) Write down the integral expression of the solution in real space as the inverse Fourier transform of Ộ(kr, ky, k2). Use the spherical coordinates to transform the integral and show that it reduces to 1 k sin(kr) º(r) dk 272r k2 + k2 c) (Bonus, o extra points) Solve this integral by extending it to the complex plane. 1*