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The scattering of free particles constrained to move on a cylindrically
symmetric curved surface is studied. The nontrivial geometry of the space
contributes to the scattering cross section through the kinetic as well as a
possible scalar curvature term in the quantum Hamiltonian. The coefficient of
the latter term is known to be related to the factor-ordering problem in
curved-space quantization. Hence, in principle, the scattering data may be
used to provide an experimental resolution of the theoretical
factor-ordering ambiguity. To demonstrate the sensitivity required of such an
experimental setup, the effect of a localized magnetic field in the scattering
process is also analyzed.
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