- #1
- 8,447
- 5,600
Homework Statement
Show that
$$
G(x,x') = \left\{ \begin{array}{ll} \frac{1}{2ik} e^{i k (x-x')} & x > x' \\ \frac{1}{2ik} e^{-i k (x-x')} & x < x' \end{array} \right.
$$
is a Green's function for the 1D Helmholtz equation, i.e.,
$$
\left( \frac{\partial^2}{\partial x^2} + k^2 \right) G(x,x') = \delta(x-x')
$$
Homework Equations
See above.
The Attempt at a Solution
I am having problems making a Dirac delta appear. I get that the first derivative is discontinuous, but the second derivative is continuous. I don't see any singularity appearing when putting the Green's function into the Helmholtz equation.
Any help appreciated.