  In this paper we consider quantum metastability in a class of moving
potentials introduced by Berry and Klein. Potential in this class has its
height and width scaled in a specific way so that it can be transformed into a
stationary one. In deriving the non-decay probability of the system, we argue
that the appropriate technique to use is the less known method of scattering
states. This method is illustrated through two examples, namely, a moving
delta-potential and a moving barrier potential. For expanding potentials, one
finds that a small but finite non-decay probability persists at large times.
Generalization to scaling potentials of arbitrary shape is briefly indicated.
