Abstract

The problem of quasi-monochromatic wave packet tunneling through a potential rectangular barrier is studied. It is shown that the approach to calculating the time delay of a wave packet called ``phase time’’ is not universally correct though well known in the literature. In this paper we discuss the mathematical reasons for this discrepancy, and substantiate another, more correct analytical method for calculating the time delay in the approximation of wide barriers. This time depends on the shape of the envelope complex wave function falling on the barrier. Analytical results for the Gaussian wave packet are presented.

Graphical abstract

中文翻译：

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时间延迟对通过势垒隧穿的波包形状的依赖性

摘要

研究了准单色波包通过潜在的矩形势垒隧穿的问题。结果表明，尽管在文献中众所周知，计算波包时间延迟的方法称为``相位时间''并不是普遍正确的。在本文中，我们讨论了造成这种差异的数学原因，并证实了另一种更正确的分析方法，用于计算宽壁垒近似中的时间延迟。该时间取决于落在屏障上的包络复波函数的形状。给出了高斯波包的分析结果。

图形概要