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arXiv · 1805.09600

Time averaging of weak values - consequences for time-energy and coordinate-momentum uncertainty

Eli Pollak·S. Miret-Artés
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Abstract

Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also find that time averaging allows one to predict in advance the momentum of a particle at a post selected point in space with accuracy greater than the limit of $\hbar /2$ as dictated by the uncertainty principle. This comes at a cost - it is not possible at the same time to predict when the particle will arrive at the post selected point. A specific example is provided for one dimensional scattering from a square barrier.

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Eli Pollak, S. Miret-Artés. 2018-05-24. Time averaging of weak values - consequences for time-energy and coordinate-momentum uncertainty. https://doi.org/10.1088/1367-2630/aad020

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