The bound states of the massless Dirac equation on the torus

Abstract

The Dirac equation on the toroidal surface is studied. The non-constant Fermi velocity functions are used in the Dirac Hamiltonian to get trigonometric Scarf and Rosen-Morse potentials using the method given in [19], then, the exact solutions are written. On the other hand, consecutive mappings are used to get a trigonometric Scarf I-like potential model and the solutions are obtained in the second part of the paper.