Exact solutions of the (2+1) Dimensional Dirac equation in a constant magnetic field in the presence of a minimal length

Abstract

We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive exact solutions for a given explicit representation of the GUP and provide expressions of the wave functions in the momentum representation. We find that in the minimal length case the degeneracy of the states is modified and that there are states that do not exist in the ordinary quantum mechanics limit (β-->0). We also discuss the mass-less case which may find application in describing the behavior of charged fermions in new materials like Graphene.

9 pages, to appear in Physical Review D

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