One-dimensional scattering by an arbitrary finite periodic potential is considered. Closed expressions for reflection and transmission (tunneling) amplitudes and probabilities are obtained. Equations determining the positions of transmission resonances are derived. The appearance of a band structure of the energy eigenspectrum as the number of barriers increases is investigated. The application of the results for the description of the reflection of X-rays incident under an angle slightly above the critical angle for total external reflection on the superlattice structures is discussed. © 1994.
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