Template:Separation of variables in two dimensions: Difference between revisions
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\phi(x,z) = X(x)Z(z) | \phi(x,z) = X(x)Z(z)\, | ||
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\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> | ||
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Revision as of 04:21, 26 August 2008
We solve 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]
