  We derive the effective one-dimensional Schrodinger-Pauli equation for
electrons constrained to move on a space curve. The electrons are confined
using a double thin-wall quantization procedure with adiabatic separation of
fast and slow quantum degrees of freedom. This procedure is capable of yielding
a correct Hermitian one-dimensional Schrodinger-Pauli operator. We find that
the torsion of the space curve generates an additional quantum geometric
potential, adding to the well-known curvature-induced one. Finally, we derive
an analytic form of the one-dimensional Hamiltonian for spin-orbit coupled
electrons in a nanoscale helical wire.
