  We study a motion of quantum particles, whose properties depend on one
coordinate so that they can move freely in the perpendicular direction. A
rotationally-symmetric Hamiltonian is derived and applied to study a general
interface formed between two semiconductors. We predict a new type of electron
states, localized at the interface. They appear whenever the two bulk
dispersions intersect. These shallow states lie near the point of intersection
and are restricted to a finite range of perpendicular momentum. The scattering
of carriers by the interface is discussed.
