Neutron-star magnetospheres are structured by very intense magnetic fields extending from 100 to $10^5\mathrm{km}$ traveled by very energetic electrons and positrons with Lorentz factors up to $\sim 10^7$. In this context, particles are forced to travel almost along the magnetic field with very small gyromotion, potentially reaching the quantified regime. We describe the state of Dirac particles in a locally uniform, constant, and curved magnetic field in the approximation that the Larmor radius is very small compared to the radius of curvature of the magnetic field lines. We obtain a result that admits the usual relativistic Landau states as a limit of null curvature. We will describe the radiation of these states, which we call quantum curvature or synchrocurvature radiation, in an upcoming paper.

• Received 26 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.085002