1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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 :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook