  The momentum operator for a spin-less particle when confined to a 2D surface
embedded into 3D space acquires a geometrical component proportional to the
mean curvature that renders it Hermitian. As a consequence, the quantum force
operator for a particle confined to spherical and cylindrical surfaces, and
free otherwise, derived by applying the Heisenberg equation of motion is found
to have an apparently no-radial component in addition to the standard classical
radial centripetal force. This component which renders the force operator
Hermitian is shown to be essential for the vanishing of the torque the force
exerts on the particle and so for the conservation of orbital angular momentum
and energy. It is demonstrated that the total force is in fact radial as should
be the case for a torque-less one and so can be identified as the quantum
centripetal force.
