  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.
