  In this work, we construct time-dependent potentials for the Schr\"odinger
equation via supersymmetric quantum mechanics. The generated potentials have a
quantum state with the property that after a particular threshold time $t_F$,
when the potential does no longer change, the evolving state becomes a bound
state in the continuum, its probability distribution freezes. After the
factorization of a geometric phase, the state satisfies a stationary
Schr\"odinger equation with time-independent potential. The procedure can be
extended to support more than one bound state in the continuum. Closed
expressions for the potential, the bound states in the continuum, and
scattering states are given for the examples starting from the free particle.
