Conditional probabilities in quantum theory, and the tunneling time controversy

Details Conditional probabilities in quantum theory, and the tunneling time controversy Conditional probabilities in quantum theory, and the tunneling time controversy

1995-02-02

arxiv.org/abs/quant-ph/9502003v1

Phys.Rev.A52:32-42,1995

Physics

Quantum Physics

11 pages, latex, 4 postscript figures separate (one w/ 3 parts)

Scientific paper

10.1103/PhysRevA.52.32

It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to Aharonov {\it et al.}, and hence describe the outcomes of real measurements made on subensembles. In particular, this approach is used to address the question of the history of a particle which has tunnelled across a barrier. A {\it gedankenexperiment} is presented to demonstrate the physically testable implications of the results of these calculations, along with graphs of the time-evolution of the conditional probability distribution for a tunneling particle and for one undergoing allowed transmission. Numerical results are also presented for the effects of loss in a bandgap medium on transmission and on reflection, as a function of the position of the lossy region; such loss should provide a feasible, though indirect, test of the present conclusions. It is argued that the effects of loss on the pulse {\it delay time} are related to the imaginary value of the momentum of a tunneling particle, and it is suggested that this might help explain a small discrepancy in an earlier experiment.

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