= Outgoing Green function for the three-dimensional Helmholtz equation
{title2=$G_k(\mathbf r,\mathbf r')=e^{ik|\mathbf r-\mathbf r'|}/(4\pi|\mathbf r-\mathbf r'|)$}
The outgoing <Green function> satisfies $(\Delta+k^2)G_k=-\delta_{\mathbf r'}$ and the <Sommerfeld radiation condition>. For time dependence $e^{-i\omega t}$, its radial phase travels outward. Away from its source it solves the homogeneous <Helmholtz equation>. At large $r$, $G_k=e^{ikr}e^{-ik\widehat{\mathbf r}\cdot\mathbf r'}/(4\pi r)+O(r^{-2})$.
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