The case of escape probability as linear in short time
Abstract
We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is liner in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behavior, quantum absorption, time of arrival, quantum measurements, and more, as will be discussed separately.
Keywords
Cite
@article{arxiv.1712.02541,
title = {The case of escape probability as linear in short time},
author = {Avi Marchewka and Zeev Schuss},
journal= {arXiv preprint arXiv:1712.02541},
year = {2018}
}
Comments
7 pages, 1 figures.Spelling and typo corrected. The appendix was removed and for further mathematical detail A. Friedman's book was referred to. Both sections (introduction and summary) have been extended (as the referee suggested). Accepted for publication at Physics Letters A