  For a particle in a box, the operator $-i\partial_x$ is not self-adjoint and
thus does not qualify as the physical momentum. As a result, in general the
Ehrenfest theorem is violated. Based upon a recently developed new concept for
a self-adjoint momentum operator, we reconsider the theorem and find that it is
now indeed satisfied for all physically admissible boundary conditions. We
illustrate these results for bouncing wave packets which first spread, then
shrink, and return to their original form after a certain revival time. We
derive a very simple form of the general Heisenberg-Robertson-Schr\"odinger
uncertainty relation and show that our construction also provides a physical
interpretation for it.
