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

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(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|x|\rightarrow\infty\mathrm{.}
 
(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|x|\rightarrow\infty\mathrm{.}
 
</math></center>
 
</math></center>
where <math>\phi^{\mathrm{{In}}}</math> is the incident potential and <math>k</math>
+
where <math>\phi^{\mathrm{{In}}}</math> is the incident potential and <math>k_0</math>
is the wave number.
+
is the imaginary wave number.

Revision as of 08:46, 24 August 2008

In two-dimensions the Sommerfeld Radiation Condition is

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

where [math]\displaystyle{ \phi^{\mathrm{{In}}} }[/math] is the incident potential and [math]\displaystyle{ k_0 }[/math] is the imaginary wave number.