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

  1. Apr 21, 2010 #1
    The differential equation is as follows:

    [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)
     
  2. jcsd
  3. Apr 23, 2010 #2
    Try working in Fourier space ;) you will get a nasty integral for the Green's function, but it looks being solvable :)
     
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