Pauli Equation on a Curved Surface and Rashba Splitting on a Corrugated Surface

The Schroedinger equation for a spinless charged particle on a curved surface under an electromagnetic field has been obtained by adopting a proper gauge which allows the separation of the on-surface and transverse dynamics. [Phys. Rev. Lett. 100 (2008) 230403] As its extension, I provide the Pauli equation for a charged spin-1/2 particle confined to a curved surface under an electromagnetic field. Energy spectra of a sphere and a corrugated surface to which a particle is confined are given as simple applications of the equation. The energy levels obtained exhibit splittings due to the relativistic effect known as the Rashba effect.