  We analyse a modified Dirac equation based on a noncommutative structure in
phase space. The noncommutative structure induces generalised momenta and
contributions to the energy levels of the standard Dirac equation. Using
techniques of perturbation theory, we use this approach to find the lowest
order corrections to the energy levels and eigenfunctions for two linear
potentials in three dimensions, one with radial dependence and another with a
triangular shape along one spatial dimension. We find that the corrections due
to the noncommutative contributions may be of the same order as the
relativistic ones.
