Passage of charged particles through a crystal in the presence of a quantum magnetic field

In this article the problem of the passage of charged particles through a crystal in the presence of a quantum magnetic field is solved. The solution of a quantum mechanical equation which describes the motion of a flux of slow particles inelastically scattered by optical phonons is found. The electron energy loss per unit length travelled inside the crystal is calculated. Also the characteristic length of energy loss due to interactions with optical phonons is calculated. (Auth.)