Topics
Electrical conduction, Fundamental constants, Recurrence relations, Educational assessment, Quantum mechanics, Scattering matrix, Quantum tunneling, Transmission probability, Public policy and governance

In a recent paper, Olsen and Vignale1 considered one-dimensional scattering by a potential consisting of a chain of N identical (nonoverlapping) “cells,” all separated by the same distance a⁠. Their main goal was to study the limit N→∞ of a potential that becomes periodic on the positive half line. This problem is not new and has been studied by many authors2–6 and references cited therein.

To study the N→∞ limit, recurrence relations were derived in Ref. 1 to allow the transmission and reflection amplitudes of the finite-periodic potential to be expressed in terms of those of its cells. Their derivation is based on the tacit assumption that it is possible to construct the transmission and reflection amplitudes by adding all the possible elementary scattering amplitudes that are associated with the different virtual paths that the particle can follow inside the potential structure,...

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