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The Hamiltonian for a spin zero particle that is confined to a curve embeddedin the 3D space is constructed by squeezing the coordinates spanning a tubenormal to the curve onto the curve assuming strong normal forces. We follow thenew approach that we applied to confine a particle to a surface, in that westart with an expression for the 3D momentum operators whose components alongand normal to the curve directions are separately Hermitian. The kinetic energyoperator expressed in terms of the momentum operator in the normal direction isthen a Hermitian operator in this case. When this operator is dropped and thethickness of the tube surrounding the curve is set to zero, one automaticallygets the Hermitian curve Hamiltonian that contains the geometric potential termas expected. It is demonstrated that the origin of this potential lies in theordering or symmetrization of the original 3D momentum operators in order torender them Hermitian. The Hermitian momentum operator for the particle as itis confined to the curve is also constructed and is seen to be similar to whatis known as the geometric momentum of a particle confined to a surface in thatit has a term proportional to the curvature that is along the normal to thecurve. The force operator of the particle on the curve is also derived, and isshown to reduce, for a curve with a constant curvature and torsion, to a --apparently -- single component normal to the curve that is a symmetrization ofthe classical expression plus a quantum term. All the above quantities are thenderived for the specific case of a particle confined to a cylindrical helixembedded in 3D space.

Hamiltonian, Geometric Momentum and Force Operators for a Spin Zero Particle on a Curve: Physical Approach