Template:Sommerfeld radiation condition three dimensions: Difference between revisions

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<center><math>
<center><math>
\sqrt{|\mathbf{r}|}\left(  \frac{\partial}{\partial|\mathbf{r}|}-k_0\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{{I}}})=0,\;\mathrm{{as\;}}|\mathbf{r}|\rightarrow\infty\mathrm{.}
</math></center>
</math></center>
where <math>\phi^{\mathrm{{In}}}</math> is the incident potential.
where <math>\phi^{\mathrm{{I}}}</math> is the incident potential.

Revision as of 09:06, 13 April 2009

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{{I}}})=0,\;\mathrm{{as\;}}|\mathbf{r}|\rightarrow\infty\mathrm{.} }[/math]

where [math]\displaystyle{ \phi^{\mathrm{{I}}} }[/math] is the incident potential.

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