  We consider basic dynamical effects in settings based on a pair of local
potential traps that may be effectively switched on and off, or suddenly
displaced, by means of appropriate control mechanisms, such as the scanning
tunneling microscopy (STM) or photo-switchable quantum dots. The same models,
based on the linear Schrodinger equation with time-dependent trapping
potentials, apply to the description of optical planar systems designed for the
switching of trapped light beams. The analysis is carried out in the analytical
form, using exact solutions of the Schrodinger equation. The first dynamical
problem considered in this work is the retention of a particle released from a
trap which was suddenly turned off, while another local trap was switched on at
a distance - immediately or with a delay. In this case, we demonstrate that the
maximum of the retention rate is achieved at a specific finite value of the
strength of the new trap, and at a finite value of the temporal delay,
depending on the distance between the two traps. Another ptoblem is retrapping
of the bound particle when the addition of the second trap transforms the
single-well setting into a double-well potential (DWP). In that case, we find
probabilities for the retrapping into the ground or first excited state of the
DWP. We also analyze effects entailed by the application of a kick to a bound
particle, the most interesting one being a kick-induced transition between the
DWP's ground and excited states. In the latter case, the largest transition
probability is achieved at particular strength of the kick.
