  In this paper we propose a self--consistent approach to the description of
temporal dynamics of localized states. This approach is based on exactly
solvable quantum mechanical models with multi-well potentials and their
propagators. States of Hamiltonians with multi-well potentials form a suitable
basis for the expansion of wave packets with different shapes and localization
degrees. We also consider properties of the tunneling wave packets, taking into
account all states of Hamiltonians with symmetric and asymmetric potentials, as
well as their dependence on the degree of localization and deformations of
potentials. The study of the dynamics of initially localized states shows that
application of the two-state approximation for the description of tunneling is
considerably limited, especially for systems, which have several states in the
under-barrier region, as for example in modern superconducting quantum
interference devices and traps for cold atoms.
