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

Abstract

The exact solutions of the (2 + 1) dimensional Dirac equation on the torus and the new extension and generalization of the trigonometric Pöschl-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.

Generalized Ellis-Bronnikov graphene wormhole

“…The electronic properties of such two-dimensional systems are highly dependent on the geometry [31][32][33], so that they can be used as analogue models for high energy physics systems [14,[34][35][36]. In addition, the effect of curvature in such two-dimensional systems opens the possibility of constructing new electronic devices based on curved graphene struc-tures has motivated the study of graphene in several curved surfaces, such as Möbius-strip [37], ripples [38], corrugated surfaces [39], catenoid [40][41][42][43], Torus [44][45][46], paraboloid [47], spheres [48], among others.…”

Interaction of molecular tori in columnar structures

“…The effects of bending of carbon nanotubes to obtain toroids are considered in [7,8]. The role of the curvature of the surface on a carbon torus is highlighted in [9] and in several other works [10][11][12]. As can be seen from [9][10][11][12], the relationship between the inner and outer radii of the tori plays a role in most properties associated with the nanotori.…”

Studying the possibility of using fullerenes inside carbon nanotubes as a molecular engine

“…Reference [5] presents the potential of the torus-atomic interaction. In works [6][7][8][9][10][11][12][13] examples of mathematical modeling of carbon nanostructures are given. in 9-10, an integral fullerene-fullerene potential was developed, which makes it possible to significantly reduce the time for calculating molecular dynamics structures that consist of spherical molecules.…”