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

Abstract

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.

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

References in corpus (3)

• Quantum mechanics and quantum Hall effect on Riemann surfaces
• Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets, Green's Functions, and a Supersymmetric Proof of the Index Theorem
• Supersymmetry and the Atiyah-Singer Index Theorem II: The Scalar Curvature Factor in the Schr{\" o}dinger Equation

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• Geometric scattering in the presence of line defects
• Holomorphic Path Integrals in Tangent Space for Flat Manifolds