A mathematically rigorous approach raises questions concerning the generalized Hartman effect

TL;DR

This paper critically examines the generalized Hartman effect, revealing that previous assumptions about tunneling time independence are mathematically unfounded, and demonstrating that tunneling time depends on the separation between barriers.

Contribution

It provides a rigorous mathematical analysis showing that tunneling time varies with barrier separation, challenging prior claims of the generalized Hartman effect.

Findings

Tunneling time depends on the distance between barriers.

Previous derivations of the generalized Hartman effect lack mathematical rigor.

Rigorous analysis contradicts earlier assumptions of tunneling time independence.

Abstract

With reference to a particle tunneling through two successive barriers, it seems to have been generally accepted that the tunneling time does not depend on the separation distance between the barriers. This phenomenon has been called the {\it generalized Hartman effect}. In this letter, we point out a lack of mathematical rigour in the reasoning by which this effect was deduced about ten years ago. A mathematically rigorous treatment shows us that the tunneling time does indeed depend on the length of the free space between the barriers.