  We derive the classical limit of quantum mechanics by describing the center
of mass of a system constituted by a large number of particles. We will show
that in that limit the commutator between the position and velocity of the
center of mass is infinitesimal, which allows both to be known with great
precision. We then show how the infinitesimal commutator allows for the
definition of functions of position and velocity, and how the commutator
reduces to a Poisson bracket.
