  Quantum escape of a particle via a time-dependent confining potential in a
semi-infinite one-dimensional space is discussed. We describe the
time-evolution of escape states in terms of scattering states of the quantum
open system, and calculate the probability $P(t)$ for a particle to remain in
the confined region at time $t$ in the case of a delta-function potential with
a time-oscillating magnitude. The probability $P(t)$ decays exponentially in
time at early times, then decays as a power later, along with a
time-oscillation in itself. We show that a larger time-oscillation amplitude of
the confining potential leads to a faster exponential decay of the probability
$P(t)$, while it can rather enhance the probability $P(t)$ decaying as a power.
These contrastive behaviors of the probability $P(t)$ in different types of
decay are discussed quantitatively by using the decay time and the power decay
magnitude of the probability $P(t)$.
