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Solid State Communications

Limitations on the use of Bohm's causal interpretation of quantum mechanics for the computation of tunneling times

Mark J. Hagmann

Published May 1, 1993• 9 citations
Publisher
DOI
10.1016/0038-1098(93)90378-z

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In Bohm's causal or trajectory interpretation of quantum mechanics, it is straightforward to determine, from a sufficiently large number of calculated particle trajectories, probability distributions for time delays caused by a potential barrier, or for transmission times through a barrier. We show that these distributions can be calculated directly and more efficiently from probability currents, without the calculation of Bohm trajectories as an intermediate step. The ideas are illustrated for Gaussian wave packets incident on a square potential barrier and used to explain why average causal delay times differ from the average delay times calculated in other approaches.
An interpretation of quantum mechanics in terms of classical concepts, ``beables,'' due to de Broglie, Bohm, and Bell (BBB) is generalized and further developed. By assuming that all physical quantities take discrete values on sufficiently small scales, we can use this interpretation to give trajectories for all possible quantities, including the position of a particle, its spin, etc. When applied to position, it is shown that, in the continuum limit, this interpretation reduces to the causal one of Bohm. As an illustration, the BBB trajectories are computed explicitly in two simple models.