Difference between revisions of "Template:Incident potential for two dimensions"
From WikiWaves
Jump to navigationJump to search| Line 10: | Line 10: | ||
</center> | </center> | ||
The first term in the expansion of the diffracted potential for the region <math>x < 0</math> is given by | The first term in the expansion of the diffracted potential for the region <math>x < 0</math> is given by | ||
| + | <center> | ||
| + | <math> | ||
| + | a_{0}e^{k_{0}x}\chi_{0}\left( | ||
| + | z\right). | ||
| + | </math> | ||
| + | </center> | ||
Revision as of 04:10, 6 March 2012
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. We would only see this in the time domain [math]\displaystyle{ \Phi(x,z,t) }[/math] however, in the frequency domain the incident potential can therefore be written as
[math]\displaystyle{ \phi^{\mathrm{I}}(x,z) =e^{-k_{0}x}\chi_{0}\left( z\right). }[/math]
The first term in the expansion of the diffracted potential for the region [math]\displaystyle{ x \lt 0 }[/math] is given by
[math]\displaystyle{ a_{0}e^{k_{0}x}\chi_{0}\left( z\right). }[/math]
