On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty

Abstract

We exactly solve the (2+1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two 2-dimensional non-relativistic harmonic oscillator and obtain the solutions without directly solving the corresponding differential equations which are presented by Menculini et al. [Phys. Rev. D 87, 065017 (2013)]. We also show that Menculini et al. solution is a subset of the general solution which is related to the even quantum numbers.