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Early times in tunneling

Gaston Garcia-Calderon·Jorge Villavicencio
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Abstract

Exact analytical solutions of the time-dependent Schrödinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value along the tunneling and transmitted regions of the potential. At the barrier width it exhibits, at early times, a distribution of traversal times that typically has a peak $τ_p$ and a width $Δτ$. Numerical results for other tunneling times, as the phase-delay time, fall within $Δτ$. The Büttiker traversal time is the closest to $τ_p$. Our results resemble calculations based on Feynman paths if its noisy behaviour is ignored.

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Gaston Garcia-Calderon, Jorge Villavicencio. 2000-08-03. Early times in tunneling. https://arxiv.org/abs/quant-ph/0008014

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