Scalar Curvature Factor in the Schroedinger Equation and Scattering on a Curved Surface

Details Scalar Curvature Factor in the Schroedinger Equation and Scattering on a Curved Surface Scalar Curvature Factor in the Schroedinger Equation and Scattering on a Curved Surface

1996-02-17

arxiv.org/abs/hep-th/9602095v2

Phys.Rev. A54 (1996) 1165-1170

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, latex. Some minor changes made, to appear in Phys. Rev. A.

Scientific paper

10.1103/PhysRevA.54.1165

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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