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American Journal of Physics

A Simple Treatment of Potential Barrier Penetration

Bernard L. Cohen

Published Feb 1, 1965• 21 citations
Publisher

Abstract

It is pointed out that the penetration of a particle through a potential barrier may be understood as a climb over the barrier during one of the energy fluctuations expected from the uncertainty principle, rather than as a “tunneling” under the barrier. A method of obtaining the quantitative result with this model is presented.
DOI
10.1119/1.1971334

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The interaction between incident and target particles is inferred from the numbers and angular distribution of scattered particles and from their energy distribution. It is important to recognize that a scattering region, as represented for example by a rectangular barrier, is a region where, in classical terms, forces are applied to the incident particles. A full analysis of scattering events must, in principle, embody the description of a localized free particle that travels toward a center of force and is scattered by it. Quantum-mechanically, that implies a theoretical analysis in terms of packet states, with an explicit account of their change of position with time. One of the most striking effects described by quantum mechanics is the transmission of incident particles across a potential barrier whose height is greater than the particle energy. Classically, these particles lack the energy to get over the barrier, yet for quantum-mechanical systems some fraction of incident particles are transmitted.