The q-deformed Dirac oscillator in 2Â +Â 1 dimensions

In this paper we obtain the Hamiltonian of Dirac oscillator in an external magnetic field in terms of q-deformed creation and annihilation operators in 2+1 dimensions. For this system, we find coordinate representations of q-deformed creation and annihilation operators, eigenvalues and eigenfunctions. We also construct the lowest Landau levels exactly by applying the q-deformed Dirac annihilation operator to the vacuum state. This system may be considered for the study of graphene in the q-deformed version.