Directly integrating the Schroedinger to determine tunneling rates for arbitrary one-dimensional potential barriers

TL;DR

This paper introduces a straightforward method for calculating tunneling probabilities in one-dimensional quantum barriers by integrating the Schrödinger equation from the transmission region backwards, making the process accessible and applicable to various potential profiles.

Contribution

It presents a novel, simple approach for directly integrating the Schrödinger equation to determine tunneling rates for arbitrary barriers, enhancing educational and practical applications.

Findings

Effective for arbitrary potential barriers

Applicable to resonant tunneling studies

Accessible to undergraduate students

Abstract

By directly integrating the Schroedinger starting in the transmission region and working backwards through the barrier, the tunneling probability can be determined for arbitrary potential barriers. The method employs techniques familiar to undergraduates and is used here to study resonant tunneling.