A spin-less particle on a rotating curved surface in Minkowski space

Abstract

In Minkowski space M, we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S. Using the thin-layer quantization formalism to constrain the particle on S, we obtain the relativity-corrected geometric potential V-g', and a novel effective potential (V) over tilde (g) related to both the Gaussian curvature and the geodesic curvature of the rotating surface. The Coriolis effect and the centrifugal potential also appear in the equation. Subsequently, we apply the surface Schrodinger equation to a rotating cylinder, sphere and torus surfaces, in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.