  We find an exact analytical solution of the reduced density matrix from the
Feynman-Vernon influence functional theory for a wave packet influenced by an
environment containing a few discrete modes. We obtain two intrinsic energy
scales relating to the time scales of the system and the environment. Different
relationship between these two scales alters the overall form of the solution
of the system. We also introduce a decoherence measure for a single wave packet
which is defined as the ratio of Schr\"odinger uncertainty over the
delocalization extension of the wave packet and characterizes the
time-evolution behavior of the off-diagonal reduced density matrix element. We
utilize the exact solution and the docherence measure to study the wave packet
decoherence dynamics. We further demonstrate how the dynamical diffusion of the
wave packet leads to non-Markovian decoherence in such a microscopic
environment.
