Dirac Equation in the Presence of Minimal Uncertainty in Momentum

In this paper, we have studied the influence of minimal uncertainty in momentum on three and two-dimensional Dirac oscillator. For the first case, the calculation is carried out analytically, the wave functions and their corresponding energy spectrum are then deduced. For the second case, the massless Dirac–Weyl electron moves with an effective Fermi velocity in graphene and subjected to the action of a uniform magnetic field is examined, the energy eigenvalues and their corresponding wave functions are determined and expressed according to the hypergeometric function. The upper bound of EUP parameter was found by comparing obtained results with experimental data. (author)