How fast do wave packets typically spread out?

[nonequilibrium]

Do the wave functions for smaller objects disperse faster?

How long does a macroscopic wave function (for example that corresponding to a measurement device) keep its broadness (roughly speaking)?

Context: I'm reading a paper where they rely on the claim

Now if, for example, we are dealing here with the
semi-classical regime for the system, an initial collection of narrow and approximately
disjoint wave packets should remain so under their evolution.

and I would have no clue about this, hence this post.

 

[jtbell]

Try playing around a bit with the formula at the end of this page:

Time Development of a Gaussian Wave Packet