  We describe a study motivated by our interest to examine the incompleteness
of the Ehrenfest's theorem in quantum mechanics and to resolve a doubt
regarding whether or not the hermiticity of the hamiltonian operator is
sufficient to justify a simplification of the expression of the
macroscopic-observable time derivative that promotes the one usually found in
quantum-mechanics textbooks. The study develops by considering the simple
quantum system "particle in one-dimensional box". We propose theoretical
arguments to support the incompleteness of the Ehrenfest's theorem in the
formulation he gave, in agreement with similar findings already published by a
few authors, and corroborate them with the numerical example of an electric
charge in an electrostatic field. The contents of this study should be useful
to Bachelor and Master students; the style of the discussions is tailored to
stimulate, we hope, the student's ability for independent thinking.
