Scalar curvature factor in the Schrödinger equation and scattering on a curved surface

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. © 1996 The American Physical Society.