A comprehensive presentation of an approach to finite periodic systems is given. The general expressions obtained here allow simple and precise calculations of various physical quantities characteristic of crystalline systems. Transmission amplitudes through n-cell multichannel quantum systems are rigorously derived. General expressions for several physical quantities are entirely expressed in terms of single-cell amplitudes and a new class of polynomials $p_{N,n}.$ Besides the general expressions, we study some superlattice properties such as the band structure and its relation to the phase coherence phenomena, the level density and the Kronig-Penney model as its continous espectrum limit. Band structure tailoring, optical multilayer systems, resonant energies and functions, and channel-mixing effects in multichannel transport processes are also analyzed in the light of this approach.

• Received 26 June 2001

DOI:https://doi.org/10.1103/PhysRevB.65.205120