  The Hamiltonian for a spin zero particle that is confined to a curve embedded
in the 3D space is constructed by squeezing the coordinates spanning a tube
normal to the curve onto the curve assuming strong normal forces. We follow the
new approach that we applied to confine a particle to a surface, in that we
start with an expression for the 3D momentum operators whose components along
and normal to the curve directions are separately Hermitian. The kinetic energy
operator expressed in terms of the momentum operator in the normal direction is
then a Hermitian operator in this case. When this operator is dropped and the
thickness of the tube surrounding the curve is set to zero, one automatically
gets the Hermitian curve Hamiltonian that contains the geometric potential term
as expected. It is demonstrated that the origin of this potential lies in the
ordering or symmetrization of the original 3D momentum operators in order to
render them Hermitian. The Hermitian momentum operator for the particle as it
is confined to the curve is also constructed and is seen to be similar to what
is known as the geometric momentum of a particle confined to a surface in that
it has a term proportional to the curvature that is along the normal to the
curve. The force operator of the particle on the curve is also derived, and is
shown to reduce, for a curve with a constant curvature and torsion, to a --
apparently -- single component normal to the curve that is a symmetrization of
the classical expression plus a quantum term. All the above quantities are then
derived for the specific case of a particle confined to a cylindrical helix
embedded in 3D space.
