Template:Sommerfeld radiation condition three dimensions: Difference between revisions

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In three-dimensions the [[Sommerfeld Radiation Condition]] is  
In three-dimensions the [[Sommerfeld Radiation Condition]] is  
<center><math>
<center><math>
\sqrt{|\mathbf{r}|}\left(  \frac{\partial}{\partial|\mathbf{r}|}-{i}k\right)
\sqrt{|\mathbf{r}|}\left(  \frac{\partial}{\partial|\mathbf{r}|}-k_0\right)
(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|\mathbf{r}|\rightarrow\infty\mathrm{.}
(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|\mathbf{r}|\rightarrow\infty\mathrm{.}
</math></center>
</math></center>

Revision as of 07:38, 24 August 2008

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]