String with Free Ends: Green's Function, Spectrum, and Completeness

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Consider the following boundary value problem:

$\displaystyle \frac{d^2u}{dx^2}+\lambda u$	$\displaystyle =$	0
$\displaystyle u'(0)$	$\displaystyle =$	0
$\displaystyle u'(\ell)$	$\displaystyle =$	$\displaystyle 0 ~~.$

Ulrich Gerlach 2010-12-09