Template:Incident potential for two dimensions: Difference between revisions

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m Reverted edits by Meylan (Talk) to last revision by Adi Kurniawan
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\phi^{\mathrm{I}}  =e^{-k_{0}x}\phi_{0}\left(
\phi^{\mathrm{I}}  =e^{-k_{0}x}\phi_{0}\left(
z\right)  
z\right)  
</math>
</center>
== Expansion of the Potential ==
Therefore the potential can
be expanded as
<center>
<math>
\phi(x,z)=e^{-{k}_0x}\phi_0(z)+\sum_{m=0}^{\infty}a_{m}e^{{k}_{m}x}\phi_{m}(z), \;\;x<0
</math>
</center>
and
<center>
<math>
\phi(x,z)=\sum_{m=0}^{\infty}b_{m}
e^{-{k}_{m}x}\phi_{m}(z), \;\;x>0
</math>
</math>
</center>
</center>

Revision as of 01:17, 7 April 2010

Incident potential

The incident potential is a wave of amplitude [math]\displaystyle{ A }[/math] in displacement travelling in the positive [math]\displaystyle{ x }[/math]-direction. The incident potential can therefore be written as

[math]\displaystyle{ \phi^{\mathrm{I}} =e^{-k_{0}x}\phi_{0}\left( z\right) }[/math]

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