Tunneling time calculations for general finite wavepackets based on the presence time formalism

TL;DR

This paper introduces a method based on the presence time formalism to calculate tunneling times for arbitrary finite wavepackets, extending previous results and enabling the analysis of time uncertainties with high accuracy.

Contribution

It develops a generalized approach for tunneling time calculation applicable to wavepackets of any shape and length, improving upon prior methods.

Findings

The tunneling time equals the average of the phase time over energy components.

The method accurately predicts tunneling times for various wavepacket shapes.

Results agree well with numerical simulations of wavepacket evolution.

Abstract

We analyze the tunneling time problem via the presence time formalism. With this method we reproduce previous results for very long wavepackets and we are able to calculate the tunneling time for general wavepackets of arbitrary shape and length. The tunneling time for a general wavepacket is equal to the average over the energy components of the standard phase time. With this approach we can also calculate the time uncertainty. We have checked that the results obtained with this approach agree extremely well with numerical simulations of the wavepacket evolution.