Title: Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force,
Abstract: In classical mechanics, a nonrelativistic particle constrained on an $N-1$
curved hypersurface embedded in $N$ flat space experiences the centripetal
force only. In quantum mechanics, the situation is totally different for the
presence of the geometric potential. We demonstrate that the motion of the
quantum particle is "driven" by not only the the centripetal force, but also a
curvature induced force proportional to the Laplacian of the mean curvature,
which is fundamental in the interface physics, causing curvature driven
interface evolution.