SCATTERING BY LOCALLY PERIODIC ONE-DIMENSIONAL POTENTIALS

One-dimensional scattering by an arbitrary finite periodic potential i s considered. Closed expressions for reflection and transmission (tunn eling) amplitudes and probabilities are obtained. Equations determinin g the positions of transmission resonances are derived. The appearance of a band structure of the energy eigenspectrum as the number of barr iers increases is investigated. The application of the results for the description of the reflection of X-rays incident under an angle sligh tly above the critical angle for total external reflection on the supe rlattice structures is discussed.