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squenshl
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Homework Statement
The Born approximation is u(xhat) = -k2/(4*pi) [tex]\int_R[/tex] exp(-i k xhat . y)m(y)ui(y) dy where R is R3.
Suppose that m is a Gaussian m(y) = Aexp(-a|y|2), where A > 0 and a > 0. Consider an incident plane wave ui(y) = exp(iky1). Calculate the far field pattern u(xhat).
Homework Equations
The Attempt at a Solution
The Fourier transform of a Gaussian is a Gaussian. So the Fourier transform of m(y) is A/(sqrt(2a)*exp(-[tex]\omega^2/4a[/tex]). I guess what I am asking is what do I do next. Am I just solving the integral (In R^3)?