WKB - Not So Bad After All

TL;DR

This paper revisits the WKB approximation for tunneling probabilities, explaining the discrepancy with standard formulas and demonstrating its accuracy with proper connection relations across a broad energy range.

Contribution

It clarifies the origin of the doubled tunneling probability and shows how to correctly apply WKB with suitable connection formulas for reliable results.

Findings

WKB approximation closely matches exact tunneling probabilities when proper connection relations are used.

The previously observed doubling of tunneling probabilities is explained by the analysis.

Proper application of WKB extends its validity over almost the entire energy spectrum.

Abstract

It was found recently that tunneling probabilities over a barrier is roughly twice as large as that given by standard WKB formula. Here we explained how this come from and showed that WKB method does give a good approximation over almost entire energy range provided that we use appropriate connection relations.