Dirac states of an electron in a circular intense magnetic field

Neutron-star magnetospheres are structured by very intense magnetic fields extending from 100 to 10 5 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 gyro-motion, 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, that we call quantum curvature or synchro-curvature radiation, in an upcoming paper.