Compact and closed expressions for the evaluation of $n$-cell transmission amplitudes, in superlattices with $N$ open channels, are written in terms of the single-cell transmission amplitudes and a set of noncommutative polynomials, which, in the one-channel case, reduce to the Chebyshev polynomials. Interesting and nontrivial features, due to channel mixing and multiple interference phenomena occurring along the $n$-cell system, emerge when applying to specific potential profiles.

• Received 20 December 1996

DOI:https://doi.org/10.1103/PhysRevLett.80.2677