Classical and quantum motion of charged particles in the vicinity of neutral surface of a magnetic field

We present results of the classical and quantum descriptions of the charged particle motion near a neutral surface of a magnetic field, where the magnetic field vanishes. Far from the neutral surface. the drift approximation is valid within the classical limit whereas the Landau description of the charged particle in the magnetic field can be used in the quantum case. In the vicinity of the neutral surface, at the distance in the classical regime less than the Larmor radius, the particle motion is nonadiabatic. Here the motion of the particle is described by the Schrodinger equation with the potential that corresponds to that of the harmonic oscillator with frequency that dependent on the particle momentum along the neutral surface.