  In this paper we investigate quantum metastability of a particle trapped in
between an infinite wall and a square barrier, with either a time-periodically
oscillating barrier (Model A) or bottom of the well (Model B). Based on the
Floquet theory, we derive in each case an equation which determines the
stability of the metastable system. We study the influence on the stability of
two Floquet states when their Floquet energies (real part) encounter a direct
or an avoided crossing at resonance. The effect of the amplitude of oscillation
on the nature of crossing of Floquet energies is also discussed. It is found
that by adiabatically changing the frequency and amplitude of the oscillation
field, one can manipulate the stability of states in the well. By means of a
discrete transform, the two models are shown to have exactly the same Floquet
energy spectrum at the same oscillating amplitude and frequency. The
equivalence of the models is also demonstrated by means of the principle of
gauge invariance.
