Applications of the potential algebras of the two-dimensional Dirac-like operators

Abstract

Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of the Hamiltonian that close centrally extended so(3), so(2,1) or oscillator algebra. The algebraic framework is used in construction of physically interesting solvable models described by (2+1) dimensional Dirac equation. It is applied in description of open-cage fullerenes where the energies and wave functions of low-energy charge-carriers are computed. The potential algebras are also used in construction of shape-invariant, one-dimensional Dirac operators. We show that shape-invariance of the first-order operators is associated with the N=4 nonlinear supersymmetry which is represented by both local and nonlocal supercharges. The relation to the shape-invariant non-relativistic systems is discussed as well.

20 pages, 4 figures; title modified, presentation simplified and extended, misprints corrected, references added; accepted in Annals of Physics

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Cited by in corpus (4)

• Curved Spacetimes and Curved Graphene: a status report of the Weyl-symmetry approach
• Twisted kinks, Dirac transparent systems and Darboux transformations
• Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications
• Supersymmetric Analysis of the Dirac-Weyl Operator within PT Symmetry