Realistic solution to the tunneling time problem

TL;DR

This paper proposes a realistic quantum mechanical explanation for tunneling time, avoiding superluminal effects, and introduces a quantum high-jumping model to resolve paradoxes in tunneling dynamics.

Contribution

It introduces a novel high-jumping model for tunneling time, challenging traditional concepts like phase and dwell times, and provides numerical calculations supporting the model.

Findings

No superluminal tunneling effect observed.

Heisenberg's energy-time uncertainty relation verified.

Quantum high-jumping model resolves tunneling paradoxes.

Abstract

There remains the old question of how long a quantum particle takes to tunnel through a potential barrier higher than its incident kinetic energy. In this article a solution of the question is proposed on the basis of a realistic explanation of quantum mechanics. The explanation implies that the tunneling particle has a certain chance to borrow enough energy from self-interference to high-jump over the barrier. The root-mean-square velocity and the effective tunneling time of an electron tunneling through a rectangular barrier are numerically calculated. No superluminal effect (Hartman effect) is found for the tunneling electron. Heisenberg's energy-time uncertainty relation for the tunneling effect is verified by calculating an introduced coefficient representing uncertainty. The present author argues that phase time, dwell time and B\"{u}tticker-Landauer time are not appropriate expressions for the actual transit time in a tunneling process. A quantum high-jumping model is presented to resolve the paradox that kinetic energy of the tunneling particle is negative and its momentum is imaginary.