  The Dirac equation is used to describe oblique spin-conserving and spin-flip
reflections of relativistic electrons from a one-dimensional potential barrier
in a vacuum. When an electron hits the barrier from an oblique direction, its
spin-up and spin-down states have different energies due to the spin-orbit
interaction and the fact that the system has a structural inversion asymmetry.
When the electron is reflected in an elastic spin-conserving process, incoming
and outgoing angles are the same. If an elastic reflection is a spin-flip
process, the outgoing angle is different from the incoming one. As a result, a
beam of incoming spin-polarized electrons is split after the reflection into
two beams. Angles and intensities of the reflected beams are calculated. Spin
splitting of energies for relativistic electrons due to the spin-orbit
interaction in an asymmetric quantum well is described.
