1209.4980 (Vit Jakubsky)

Potential algebras of low-dimensional Dirac operators: applications    [PDF]

Vit Jakubsky

Potential algebras can be used effectively in the analysis of quantum systems described by (2+1) dimensional Dirac equation. We find integrals of motion of massless separable Dirac operator. They close centrally extended so(3), so(2,1) or oscillator algebra. The algebraic framework is used in construction of physically interesting solvable models. It is applied in description of open-cage fullerenes where the energies and wave functions of low-energy charge carriers are computed. Besides, the potential algebras are applied in the context of one-dimensional, both relativistic and non- relativistic, shape-invariant quantum systems. We show that shape-invariance of the considered Dirac operators is associated with the nonlinear N=2 supersymmetry. The potential algebra is used in construction of non- relativistic, shape-invariant systems with position dependent mass. We demonstrate that solvability of these models is associated with their N=8 supersymmetry.

View original: http://arxiv.org/abs/1209.4980