Difference between revisions of "Template:Separation of variables in two dimensions"

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We solve express the potential as
+
We express the potential as
 
<center>
 
<center>
 
<math>
 
<math>
\phi(x,z) = X(x)Z(z)
+
\phi(x,z) = X(x)Z(z)\,
 
</math>
 
</math>
 
</center>
 
</center>
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<center>
 
<center>
 
<math>
 
<math>
\frac{X^{\prime\prime}}{X} = - \frac{Z{\prime\prime}}{Z} = k^2  
+
\frac{X^{\prime\prime}}{X} = - \frac{Z^{\prime\prime}}{Z} = k^2  
 
</math>
 
</math>
 
</center>
 
</center>

Latest revision as of 11:09, 7 September 2008

We express the potential as

[math]\displaystyle{ \phi(x,z) = X(x)Z(z)\, }[/math]

and then Laplace's equation becomes

[math]\displaystyle{ \frac{X^{\prime\prime}}{X} = - \frac{Z^{\prime\prime}}{Z} = k^2 }[/math]