Early times in tunneling

Details Early times in tunneling Early times in tunneling

2000-08-03

arxiv.org/abs/quant-ph/0008014v1

Physics

Quantum Physics

4 pages, 2 figures

Scientific paper

Exact analytical solutions of the time-dependent Schr\"odinger 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 $\tau_p$ and a width $\Delta \tau$. Numerical results for other tunneling times, as the phase-delay time, fall within $\Delta \tau$. The B\"uttiker traversal time is the closest to $\tau_p$. Our results resemble calculations based on Feynman paths if its noisy behaviour is ignored.

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