  A nonrelativistic quantum mechanical particle moving freely on a curved
surface feels the effect of the nontrivial geometry of the surface through the
kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami
operator, and a geometric potential, which is a linear combination of the mean
and Gaussian curvatures of the surface. The coefficients of these terms cannot
be uniquely determined by general principles of quantum mechanics but enter the
calculation of various physical quantities. We examine their contribution to
the geometric scattering of a scalar particle moving on an asymptotically flat
embedded surface. In particular, having in mind the possibility of an
experimental realization of the geometric scattering in a low density electron
gas formed on a bumped surface, we determine the scattering amplitude for
arbitrary choices of the curvature coefficients for a surface with global or
local cylindrical symmetry. We also examine the effect of perturbations that
violate this symmetry and consider surfaces involving bumps that form a
lattice.
