2D self-interacting magnetically confined electrons

We investigate the nonlinear dynamics of electrons in the presence of an external homogeneous magnetic field in 2 + 1 flat space-time dimensions. Two regimes of magnetic fields are examined: high laboratory fields and strong-QED fields. We provide the (nonlinear) ground-state Landau energy levels together with their respective eigenfunctions. We comment on the relevance of this (toy) model to reveal certain processes thought to occur near the surfaces of neutron stars.