The differential equation is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

[d/dx^2 + k^2 - tau * dirac_delta(x-x') ] * G(x,x') = dirac_delta(x-x')

where tau is a complex valued scattering strength, and assuming scattering waves at infinity. The problem asks to derive the solution to this equation.

I've looked over Green's function theory, and I'm stumped. I don't think I can use a closed form solution or Sturm Liouville theory because of the impact of the delta function.

Would it be related to transforming the dirac delta function? something like...

dirac_delta(x-x') = 1/(sqrt(2*pi)*int( 1/(sqrt(2*pi)*e^[j*Beta*x'])*e^[-j*Beta*x],-inf,inf,Beta)

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# Homework Help: Green's function: Dirac-delta point scatterer where point sorce is located

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