Talk:Eigenfunction Matching for a Finite Dock

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Expression of the potential under the dock

It seems that the eigenfunctions [math]\displaystyle{ \frac{L\pm x}{2L}\psi_{0}(z) }[/math] do not satisfy the Laplace equation. Nor do any linear combination of them so it seems to me that we have to write [math]\displaystyle{ b_0=c_0=0 }[/math] which means removing them from the potential expression.

Eigenfunctions [math]\displaystyle{ \frac{L\pm x}{2L} }[/math] work better but they will cause problems for infinite depth...