A Wave Packet Approach to Resonant Scattering

TL;DR

This paper investigates resonant scattering in one-dimensional models using wave packets, revealing how resonance deteriorates with narrower wave packets and providing an approximate wave function that aligns well with numerical results.

Contribution

It introduces an approximate wave function for transmitted and reflected waves in resonant scattering, bridging wave packet and plane wave approaches, with validation against numerical calculations.

Findings

Resonance deteriorates as wave packet width decreases.

Approximate wave function closely matches numerical results.

Insight into the scattering process from combined analytical and numerical methods.

Abstract

Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with finite width to illustrate the deterioration of resonance with decreasing wave packet width, and suggest an approximate wave function for the transmitted and reflected components, derived from aspects of both the wave packet and plane wave approaches. A comparison with exact numerical calculations shows excellent agreement, and provides insight into the scattering process.