Scattering from a locally periodic potential

Abstract

One-dimensional scattering from a series of delta-function barriers is considered, in the context of nonrelativistic quantum mechanics. A surprisingly simple closed-form expression for the transmission probability is obtained, and compared with the earlier result of Kiang [Am. J. Phys. 42, 785–787 (1974)]. The band structure characteristic of periodic potentials emerges even when the number of barriers is quite small. However, the ‘‘saturation’’ phenomenon identified by Lee, Zysnarski, and Kerr [Am. J. Phys. 57, 729–734 (1989)] is found to depend on the energy regime in question.