Discrete uncertainty principles and Virial identities

In this paper we review the Heisenberg uncertainty principle in a discrete setting and, as in the classical uncertainty principle, we give it a dynamical sense related to the discrete Schrödinger equation. We study the convergence of the relation to the classical uncertainty principle, and, as a counterpart, we also obtain another discrete uncertainty relation that does not have an analogous form in the continuous case. Moreover, in the case of the Discrete Fourier Transform, we give an inequality that allows us to relate the minimizer to the Gaussian.