Wave and Particle Limit for Multiple Barrier Tunneling

TL;DR

This paper investigates the transition between wave and particle descriptions in quantum tunneling through multiple barriers, demonstrating resonance phenomena and deriving known results for three and four barriers.

Contribution

It applies a particle approach to multi-barrier tunneling, connecting it with wave results and numerically illustrating the transition between the two regimes.

Findings

Resonance and transparency in twin tunneling are confirmed.

Known resonance conditions for three and four barriers are derived.

Numerical transition from wave to particle limit is demonstrated.

Abstract

The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the plane wave results. In particular, the existence of resonance/transparency for twin tunnelling in the wave limit is immediately obvious. The known resonances for three and four barriers are also derived. The transition from the wave limit to the particle limit is exhibit numerically.