The bound states of the massless Dirac equation on the torus

TL;DR

This paper investigates the solutions of the massless Dirac equation on a torus, deriving exact solutions for specific potential models using advanced mathematical methods, contributing to the understanding of quantum states on curved surfaces.

Contribution

It introduces new exact solutions for the Dirac equation on a torus with non-constant Fermi velocity, employing trigonometric potentials and mapping techniques.

Findings

Exact solutions for Dirac equation with trigonometric potentials

Derivation of bound states on a toroidal surface

Application of mapping methods to potential models

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.