  We consider multiple collisions of quantum wave packets in one dimension. The
system under investigation consists of an impenetrable wall and of two
hard-core particles with very different masses. The lighter particle bounces
between the heavier one and the wall. Both particles are initially represented
by narrow Gaussian wave packets. A complete analytical solution of this problem
is presented on the basis of a new method. The idea of the method is to
decompose the two-particle wave function into a continuous superposition of
terms (channels), such that the multiple collisions within each channel do not
lead to subsequent entanglement between the two particles. For each channel,
the time evolution of the two-particle wave function is completely determined
by the motion of the corresponding classical point-like particles; therefore
the whole quantum problem is reduced to a classical calculation. The
calculation based on the above method reveals the following unexpected result:
The entanglement between the two particles first increases with time due to the
collisions, but then it begins to decrease, disappearing completely when the
light particle becomes too slow to catch up with the heavy one.
