Single point potentials with total resonant tunneling

TL;DR

This paper investigates sharply localized one-dimensional potentials with multi-layer structures, revealing conditions for total resonant tunneling and their unique energy-dependent resonance behaviors.

Contribution

It introduces exactly solvable models of multi-layer potentials that exhibit total resonant tunneling at discrete strength values, expanding understanding of quantum tunneling phenomena.

Findings

Sharp peaks of total transmission at specific potential strengths

Models behave as perfect reflectors outside resonance conditions

Resonance behavior differs from typical double barrier structures

Abstract

Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar tunneling properties are studied in considerable detail. Particularly, in the zero-range limit when the potentials are squeezed to a single point, sharp peaks with total transmission are observed at certain (positive and negative) quantized values of the potential strength constant forming infinite discrete sets. Beyond these sets, the barrier-well structures behave as a perfectly reflecting wall. The transcendental equations with respect to potential strengths, the solutions of which determine transmission (resonance) sets, are derived. In this regard, both the models are exactly solvable. The energy dependence of an incident particle is shown to reveal a resonance behavior, being completely different from that observed in a typical double barrier structure.