Template:Sommerfeld radiation condition three dimensions

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In three-dimensions the Sommerfeld Radiation Condition is

[math]\displaystyle{ \sqrt{|\mathbf{r}|}\left( \frac{\partial}{\partial|\mathbf{r}|}-k_0\right) (\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|\mathbf{r}|\rightarrow\infty\mathrm{.} }[/math]