Discrete Uncertainty Principles and Virial Identities

Abstract

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 a inequality that allows us to relate the minimizer to the Gaussian.

arXiv comment31 pages, 2 figures