  We consider one particle confined to a deformed one-dimensional wire. The
quantum mechanical equivalent of the classical problem is not uniquely defined.
We describe several possible hamiltonians and corresponding solutions for a
finite wire with fixed endpoints and non-vanishing curvature. We compute and
compare the disparate eigenvalues and eigenfunctions obtained from different
quantization prescriptions. The JWKB approximation without potential leads
precisely to the square well spectrum and the coordinate dependent stretched or
compressed box related eigenfunctions. The geometric potential arising from an
adiabatic expansion in terms of curvature is at best only valid for very small
curvature.
