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

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