  We study the temporal formation of quantum mechanical bound states within a
one-dimensional attractive square-well potential, by first solving the
time-independent Schroedinger equation and then study a time dependent system
with an external time-dependent potential. For this we introduce Gaussian
potentials with different spatial and temporal extensions, and generalize this
description also for subsequent pulses and for random, noisy potentials. Our
main goal is to study the time scales, in which the bound state is populated
and depopulated. Particularly we clarify a likely connection between the
uncertainty relation for energy and time and the transition time between
different energy eigenstates. We demonstrate, that the formation of states is
not delayed due to the uncertainty relation but follows the pulse shape of the
perturbation. In addition we investigate the (non-)applicability of first-order
perturbation theory on the considered quantum system.
