One-dimensional scattering by a locally periodic potential

Abstract

One-dimensional scattering of a particle or a wave packet by a finite number of periodic potential barriers is studied. The fundamental physical mechanism that determines the transmission coefficient is shown to be quantum interference between waves with different numbers of inner reflections. The tendency of the transmission coefficient to saturate with respect to an increase in the number of barriers is due to the free-particle nature of a particle subject to a completely periodic potential.

Quantum waveguide transport in serial stub and loop structures

“…As we increase N (the total number of stubs) to say 5, the stub lengths being the same, the sharp drops become extended to forbidden bands. In a recent study on locally periodic potential, saturation effect has been discussed [24].…”

Wave packet scattering from time-varying potential barriers in one dimension

“…The reflectivity and transmission of locally periodic potentials have been studied analytically and numerically. [23][24][25] This class of potentials is characterized by a small number of repeating units. One of the reasons for examining the transmission and reflection properties of such potentials, in contrast to a periodic potential which is infinite in extent, is that it can be an efficient means to access numerically the precursors of the properties of periodic potentials, such as band structure.…”

One-dimensional scattering: Recurrence relations and differential equations for transmission and reflection amplitudes

“…The last equalities in (9), (10) were obtained using (4), (5), and (8). The subscripts L (R) here and below denote the physical quantities of the particles incident from the left (right).…”

“…(See also [8,15]. ) In this approach the scattering process is viewed as consisting of a sequence of re6ections and transmissions occurring at each barrier.…”

“…3) is of significant interest because it exhibits the important features of quantum mechanics: tunneling and interference [8,9]. The solution of the problem manifests the origin of the band energy spectrum of periodic potentials -Brillouin zones and forbidden energy gapsas the number of scattering centers grows, making thus a bridge between atomic scattering (one center) and solidstate physics (n -+ oo, semi-infinite periodic chain).…”