  We study quantum mechanics on a curved wire by approximating the physics
around the curved region by three parameters coming from the boundary
conditions given by the two interval Sturm-Liouville theory. Since the
geometric potential on a highly curved wire is strong an non-integrable, these
parameters depend on the regularization of the curved wire. Hence, unless we
know precisely the shape of the wire, the presented method becomes not only a
useful approximation, but also a necessary scheme to deal with quantum
mechanics on highly curved wires.
