Inhomogeneous Helmholtz equation

[Aboud2002]

Homework Statement

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

Homework Equations

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

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

 

[Aboud2002]

Someone helps me in hints to satisfy the helmholtz inhomogenous equa..:'(((