Sphere on a plane: Two-dimensional scattering from a finite curved region
arXiv:2205.09603 · doi:10.1103/PhysRevA.106.042216
Abstract
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we consider a simple case of piecewise uniform curvature: a particle moves on a plane with a spherical extrusion. Depending on the latitude at which the sphere joins the plane, the extrusion can range from an infinitesimal bump to a nearly full sphere that just touches the plane. Free classical motion on this surface of piecewise uniform curvature follows geodesics that are independent of velocity, while quantum mechanical scattering depends on energy. We compare classical, semi-classical, and fully quantum problems, which are all exactly solvable, and show how semi-classical analysis explains the complex quantum differential cross section in terms of interference between two classical trajectories: the sphere on a plane acts as a kind of double slit.
arXiv comment16 pages, 10 figures
References in corpus (8)
- Graphene wormholes: A condensed matter illustration of Dirac fermions in curved space
- Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface
- Quantum phase-space representation for curved configuration spaces
- Unified description of Dirac electrons on a curved surface of topological insulators
- Geometric momentum for a particle constrained on a curved hypersurface
- Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects
- Quantum dynamics of a particle constrained to lie on a surface
- Scattering due to geometry: The case of a spinless particle moving on an asymptotically flat embedded surface