  Quantum mechanical equations of motion are obtained for particles and spin in
media with polarized electrons in the presence of external fields. The motion
of electrons and their spins is governed by the exchange interaction, while the
motion of positrons and their spins is governed by the annihilation
interaction. The equations obtained describe the motion of particles and spin
in both magnetic and nonmagnetic media. The evolution of positronium spin in
polarized media is investigated. Media with polarized electrons can be used for
polarization of positronium beams.
