Since a momentum eigenstate has a precisely defined momentum,
the
Uncertainty Principle tells us that its position is completely uncertain; it
must extend throughout all space. This
is not a good model of actual particles, which are usually localized. A more
useful wave function consists of a mixture of such momentum states. Since each
component is a ``wave'', the resulting sum is called a ``wave packet'', and can
be confined to a limited region of space. Here is a video of the time
evolution of a wave packet.
YouTube Video

The packet begins as a purely real Gaussian, located on the right side of a
quadratic potential well. The potential causes the packet to accelerate to the
left, until it reaches the bottom of the quadratic well. It then decelerates as
it moves up the left side of the well, finally stopping, and returning to the
right.

Jerome Berryhill
2013-05-09