Discrete Uncertainty Principles and Virial Identities

2014/02/20 by Aingeru Fernández-Bertolin, Fernández-Bertolin, Aingeru
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1402.5016

31 pages, 2 figures

arxiv created 2014/11/03 · arxiv updated 2014/11/04

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.

Related

• Uncertainty Relation for the Discrete Fourier Transform
• Do the Robertson-SCHRÖDINGER and the Heisenberg Uncertainty Relations Imply a General Physical Principle ?
• The uncertainty principle: variations on a theme
• A discrete Hardy's Uncertainty Principle and discrete evolutions
• Uncertainty principle for solutions of the Schrödinger equation on the Heisenberg group