Dynamics in noncentral potentials

The study of fluctuations and diffusion on surfaces with geometries without spherical symmetry can sometimes be daunting due to nontrivial forms acquired by the relevant transport equation. Since there is structural similarity between solutions of the Schroedinger equation and the diffusion equation, we highlight some exact results for the Smorodinsky-Winternitz classes of noncentral potentials with dynamical symmetries that may be used for diffusion in geometries such as tori and wedges.