Quantum mechanics on curved 2D systems with electric and magnetic fields
Quantum Physics
2009-04-14 v1 Mesoscale and Nanoscale Physics
Abstract
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the well-known geometric potential. The electric and magnetic fields are included via the four-potential. We find that there is no coupling between the fields and the surface curvature and that, with a proper choice of the gauge, the surface and transverse dynamics are exactly separable. Finally, the Hamiltonian for the cylinder, sphere and torus are analytically derived.
Cite
@article{arxiv.0803.2670,
title = {Quantum mechanics on curved 2D systems with electric and magnetic fields},
author = {Giulio Ferrari and Giampaolo Cuoghi},
journal= {arXiv preprint arXiv:0803.2670},
year = {2009}
}