Dirac Equation on the Torus and Rationally Extended Trigonometric Potentials within Supersymmetric QM

TL;DR

This paper derives exact solutions for the Dirac equation on a torus and introduces extended trigonometric potentials using supersymmetric quantum mechanics and Lie algebraic methods, providing new analytical insights.

Contribution

It presents novel exact solutions for the Dirac equation on a torus and extends trigonometric potentials using supersymmetric and algebraic techniques, unifying different approaches.

Findings

Exact solutions for Dirac equation on the torus

Extended trigonometric potentials derived

Spectrum solutions via Lie algebra match exact results

Abstract

The exact solutions of the (2+1) dimensional Dirac equation on the torus and the new extension and generalization of the trigonometric Poschl-Teller potential families in terms of the torus parameters are obtained. Supersymmetric quantum mechanical techniques are used to get the extended potentials when the inner and outer radii of the torus are both equal and inequal. In addition, using the aspects of the Lie algebraic approaches, the iso(2; 1) algebra is also applied to the system where we have arrived at the spectrum solutions of the extended potentials using the Casimir operator that matches with the results of the exact solutions.