One-dimensional quantum interference

A general analysis of scattering in finitely periodic one-dimensional potentials is considered. Using a previously developed method of potential segmentation, the authors factor out exactly the effect due to the period multiplicity via polynomials which are insensitive to the shape of a generic potential cycle and correlate the transmission resonances with the zeros of these polynomials. In the limit of infinite period multiplicity, the standard results of band structure are regained. Numerical examples are given to illustrate applicability to potentials of arbitrary shape.