A new mathematical model of tunnelling and the Hartman effect puzzle

TL;DR

This paper introduces a refined mathematical model for one-dimensional scattering that accurately describes subprocesses and resolves the Hartman effect puzzle by aligning with special relativity.

Contribution

The paper develops a new model of scattering that provides a consistent description of subprocesses and addresses the Hartman effect puzzle.

Findings

Model aligns group, dwell, and Larmor times with special relativity

Resolves the Hartman effect puzzle

Provides an individual description of transmission and reflection processes

Abstract

In this paper we develop and refine our recent model of a one-dimensional completed scattering, which gives an individual description of the transmission and reflection subprocesses at all stages of scattering. We show that the group, dwell and Larmor characteristic times, introduced in this model for the subprocesses, are in a full agreement with special relativity and allow us to solve the Hartman effect puzzle.