Difference between revisions of "Template:Sommerfeld radiation condition three dimensions"

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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}|}-k_0\right)
+
\sqrt{|\mathbf{r}|}\left(  \frac{\partial}{\partial|\mathbf{r}|} - \mathrm{i} k \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{{I}}}</math> is the incident potential.

Latest revision as of 22:27, 29 April 2010

In three-dimensions the Sommerfeld Radiation Condition is

[math]\displaystyle{ \sqrt{|\mathbf{r}|}\left( \frac{\partial}{\partial|\mathbf{r}|} - \mathrm{i} k \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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