Space Translations and Momentum

This is the first of three chapters devoted to introducing the basic dynamical variables, i.e. momentum, energy, and angular momentum as generators of space–time symmetry transformations. Firstly, the position variable will be postulated as physical observable, as empirically proven, e.g., in the two-slit experiment. Then, the momentum will be introduced as a generator of the space translations and its properties discussed, including the eigenvalue equations. Finally, the Heisenberg uncertainty principle will be deduced, as a consequence of the non-commutativity between the position and momentum operators.