Note on the Uncertainty Principle and Barrier Penetration

James S. Marsh

Bernard L. Cohen

It is pointed out that the penetration of a particle through a potential barrier may be understood as a climb over the barrier during one of the energy fluctuations expected from the uncertainty principle, rather than as a “tunneling” under the barrier. A method of obtaining the quantitative result with this model is presented.

A. Gamba

Mark J. Hagmann

Barrier penetration is attributed to energy fluctuations expected from the uncertainty principle. Numerical simulations are made by calculating the traversal time and action for a large number of possible velocity profiles. Distributions of traversal time are determined by assuming that the probability of each velocity profile decreases exponentially with the action of the fluctuation it requires. Distributions of traversal times are reported for rectangular barriers having different sizes. For large barriers the distributions are leptokurtic and centered at the semiclassical traversal time T0 = d√m/[2(V0−E)], where d and V0 are the length and height of the barrier and m and E are the mass and energy of the particle. The kurtosis decreases and the mode shifts to shorter durations with decreasing barrier size.

Alojz Kodre, Janez Strnad

A previous calculation (see J.Phys. A:Math. Gen., vol.8, p.533 (1975)) of delay time in electromagnetic barrier penetration is improved using a simple device for elimination of non-causal effects.

Steven Matthysse