Comment on "Quantum mechanical versus semiclassical tunneling and decay times"

TL;DR

This paper proposes a simplified method for calculating quantum tunneling lifetimes that accounts for bound states, demonstrating its effectiveness and the impact of bound states on particle lifetime.

Contribution

It introduces a simplified approach using <t^2>^(1/2) for lifetime calculation, which is exact without bound states and approximate with bound states, improving analysis of tunneling times.

Findings

The new method simplifies lifetime calculations.

Results are exact without bound states.

Presence of bound states significantly affects lifetime estimates.

Abstract

Shegelski, Kavka, and Hynbida have developed a method for calculating the lifetime of a particle initially localized in a potential well exactly quantum mechanically by employing a heuristic expression for the lifetime <t>. Their method allows for the inclusion of a bound state, and their results for tunneling through a centrifugal barrier demonstrate the major role that bound states play in determining the lifetime. In this comment, I show that one can greatly simplify the analysis by calculating <t^2>^(1/2) instead. Results obtained are exact when no bound state is present. In the presence of a bound state the results are only approximate but still illustrate the influence that the presence of a bound state has on the lifetime.