One-dimensional outgoing Green function
= One-dimensional outgoing Green function
For positive $k$, $e^{ik|x-x'|}$ is outgoing on both sides of $x'$ and obeys
$$
\left(\frac{d^2}{dx^2}+k^2\right)e^{ik|x-x'|}=2ik\delta(x-x').
$$
= One-dimensional outgoing Green function
For positive $k$, $e^{ik|x-x'|}$ is outgoing on both sides of $x'$ and obeys
$$
\left(\frac{d^2}{dx^2}+k^2\right)e^{ik|x-x'|}=2ik\delta(x-x').
$$