Coupling curvature to a uniform magnetic field: An analytic and numerical study

The Schrodinger equation for a spinless electron near an azimuthally symmetric curved surface Sigma in the presence of an arbitrary uniform magnetic field B is developed. A thin-layer quantization procedure is implemented to bring the particle onto Sigma, leading to the well-known geometric potential V-C proportional to h(2)-k and a second potential that couples A(N), the component of A normal to Sigma to mean surface curvature, as well as a term dependent on the normal derivative of A(N) evaluated on Sigma. Numerical results in the form of ground-state energies as a function of the applied field in several orientations are presented for a toroidal model.