One-dimensional quantum interference

Abstract

A general analysis of scattering in finitely periodic one-dimensional potentials is considered. Using a previously developed method of potential segmentation, the authors factor out exactly the effect due to the period multiplicity via polynomials which are insensitive to the shape of a generic potential cycle and correlate the transmission resonances with the zeros of these polynomials. In the limit of infinite period multiplicity, the standard results of band structure are regained. Numerical examples are given to illustrate applicability to potentials of arbitrary shape.

Resonant Tunneling and Band Mixing in Multichannel Superlattices

“…[1][2][3]. Although transmission probabilities for finite one-dimensional potentials have been routinely calculated since the early days of quantum mechanics [4], few analytic expressions for finite periodic chains are known [5,6]. Although these expressions are valuable, they are restricted to one-channel, transversely invariant or strictly 1D systems.…”

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

“…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).…”

Scattering in abrupt heterostructures using a position dependent mass Hamiltonian

“…One dimensional quantum wells (QW) and their analysis have played an increasingly significant role in various applications as well as the understanding of the properties of a variety of semiconductor devices [1,2,3,4]. The motivation for studying these problems is the recent developments in the nanofabrication of semiconductor devices, where one observes QW with very thin layers [5].…”