Resonant Tunneling

  • Lev I. Deych
Chapter

Abstract

In Sects. 6.2 and 6.3 of Chap. 6, I introduced one-dimensional quantum mechanical models, in which potential energy of a particle was described by a simplest piecewise constant function (or its extreme case—a delta-function), defining a single potential well or barrier. A natural extension of this model is a potential energy profile corresponding to several wells and/or barriers (or several delta-functions). In principle, one can approach the multi-barrier problem in the same way as a single well/barrier situation: divide the entire range of the coordinate into regions of constant potential energy, and use the continuity conditions for the wave function and its derivative to “stitch” the solutions from different regions. However, it is easier said than done. Each new discontinuity point adds two new unknown coefficients and correspondingly two equations. If in the case of a single barrier you had to deal with the system of four equations, a dual-barrier problem would require solving the system of eight equations, and soon even writing those equations down becomes a serious burden, and I do not even want to think about having to solve them.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Lev I. Deych
    • 1
  1. 1.Physics Department, Queens College and the Graduate CenterCity University of New YorkNew YorkUSA

Personalised recommendations