The wave packets we tried above satisfy an uncertainty principle which is a property of waves. That is .
For the ``square'' packet the full width in
The width in
is a little hard to define, but, lets use the first node in the probability
So the width is twice this or
This gives us
For the Gaussian wave packet, we can rigorously read the RMS width of the probability distribution as was done at the end of the section on the Fourier Transform of a Gaussian.
If we translate into momentum
If we try to localize a particle to a very small region of space, its momentum becomes uncertain. If we try to make a particle with a definite momentum, its probability distribution spreads out over space.
Jim Branson 2013-04-22