Analysis of wavepacket tunneling with the method of Laplace transformation

TL;DR

This paper applies Laplace transformation to analyze wavepacket tunneling, revealing a sequence of transmitted wave packets and providing insights into tunneling time phenomena like the Hartmann effect.

Contribution

It introduces a novel application of Laplace transformation to study wavepacket tunneling dynamics, offering new explanations for tunneling time effects.

Findings

Transmitted wave packet can be decomposed into multiple wave packets.

Provides a new perspective on the Hartmann effect.

Offers potential explanation for experimental tunneling results.

Abstract

We use the method of Laplace transformation to determine the dynamics of a wave packet that passes a barrier by tunneling. We investigate the transmitted wave packet and find that it can be resolved into a sequence of subsequent wave packages. This result sheds new light on the Hartmann effect for the tunneling time and gives a possible explanation for an experimental result obtained by Spielmann et. al.