Channeling of relativistic electrons and positrons

The quanta-mechanical problem of relativistic electron (positron) movement through the electro-static crystal field for the case of small angle between initial particle momentum and the atomic plane is considered for the case of electron energy larger than several MeV. The analytical expressions for the wave functions for electrons and positrons in the model potentials, which are similar to the state of the 'one-dimensional relativistic atom', are presented.