Bouncing wave packets, Ehrenfest theorem, and uncertainty relation based upon a new concept for the momentum of a particle in a box

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