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Solid State Communications

Transmission, reflection and dwell times within Bohm's causal interpretation of quantum mechanics

C. Richard Leavens

Published Jun 1, 1990• 72 citations
Publisher
DOI
10.1016/0038-1098(90)90457-m

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Dwell times for transmission and reflection

Nikolay Leonidovich Chuprikov

As was shown in quant-ph/0405028, the state of a tunneling particle can be uniquely presented as a coherent superposition of two states to describe alternative sub-processes, transmission and reflection. In this paper, on the basis of the stationary wave functions for these sub-processes, we give new definitions of the dwell times for transmission and reflection. In the case of rectangular potential barriers the dwell times are obtained explicitly. In contrast with the well-known Büttiker's dwell-time, our dwell time for transmission increases exponentially, for the under-barrier tunneling, with increasing the barrier's width. By our approach the well-known Hartman effect is rather an artifact resulted from an improper interpretation of the wave-packet tunneling and experimental data, but not a real physical effect accompanying the tunneling phenomenon.

arXiv:quant-ph/0502073•Feb 14, 2005•2 citations
Several practical implications of the noncrossing property of one-dimensional Bohm trajectories are examined. It is shown that the position of a Bohm particle, the average transmission, reflection and dwell times, and the probability distribution of these tunneling times, can all be obtained without actually calculating trajectories. On the other hand, the intuitive interpretation of the scattering of wave packets by potential barriers is discussed within the framework of Bohm's interpretation of quantum mechanics. In this regard, claims that Bohm's approach leads to counterintuitive results are shown to be subjective. \textcopyright{} 1996 The American Physical Society.
As was shown in quant-ph/0405028, the state of a tunneling particle can be uniquely presented as a coherent superposition of two states to describe alternative sub-processes, transmission and reflection. In this paper, on the basis of the stationary wave functions for these sub-processes, we give new definitions of the dwell times for transmission and reflection. In the case of rectangular potential barriers the dwell times are obtained explicitly. In contrast with the well-known Büttiker's dwell-time, our dwell time for transmission increases exponentially, for the under-barrier tunneling, with increasing the barrier's width. By our approach the well-known Hartman effect is rather an artifact resulted from an improper interpretation of the wave-packet tunneling and experimental data, but not a real physical effect accompanying the tunneling phenomenon.