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We analyse a modified Dirac equation based on a noncommutative structure inphase space. The noncommutative structure induces generalised momenta andcontributions to the energy levels of the standard Dirac equation. Usingtechniques of perturbation theory, we use this approach to find the lowestorder corrections to the energy levels and eigenfunctions for two linearpotentials in three dimensions, one with radial dependence and another with atriangular shape along one spatial dimension. We find that the corrections dueto the noncommutative contributions may be of the same order as therelativistic ones.

Perturbative calculation of energy levels for the Dirac equation with generalised momenta