  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.
