Snake orbits and related magnetic edge states

We study the electron motion near magnetic field steps at which the strength and/or sign of the magnetic field changes. The energy spectrum for such systems is found and the electron states (bound and scattered) are compared with their corresponding classical paths. Several classical properties such as the velocity parallel to the edge, the oscillation frequency perpendicular to the edge and the extent of the states are compared with their quantum mechanical counterparts. A class of magnetic edge states is found which do not have classical counterparts.