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Inhomogeneous Helmholtz equation

  1. Jan 28, 2012 #1
    1. The problem statement, all variables and given/known data

    it is stated in wikipedia http://en.wikipedia.org/wiki/Helmholtz_equation

    that "Here, G is the Green's function of this equation, that is, the solution to the inhomogeneous Helmholtz equation with ƒ equaling the Dirac delta function, so G satisfies

    [del^2 + K^2]G(x)=-δ(x)

    where G(x)={i exp[ik*magnitude of x]}/2K



    2. Relevant equations

    I tried to satisfy this differential equation but I couldn't,

    3. The attempt at a solution

    First we have G(x)={iexp[ik*maginude of x]}/2k

    I defined G(x) into two intervals when x>0 G will have + sign
    when x<0 G will have - sign

    so the first derivative will be G'(x)= -{exp[ikx]}/2

    G''(x) = -ik{exp[ikx]}/2

    if I took G''+k^2G it will give me zero not -δ(x) how I can reach the right handside of Inhomogeneous Helmholtz equation

    someone give me hint
     
  2. jcsd
  3. Jan 28, 2012 #2
    Someone helps me in hints to satisfy the helmholtz inhomogenous equa..:'(((
     
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