Position-momentum uncertainty relations based on moments of arbitrary order

Steeve Zozor, Mariela Portesi, Pablo Sanchez-Moreno, and Jesus S. Dehesa

Phys. Rev. A 83, 052107 – Published 6 May 2011

Abstract

The position-momentum uncertainty-like inequality based on moments of arbitrary order for $d$ -dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by use of the Rényi-entropy-based uncertainty relation. The accuracy of the resulting lower bound is physico-computationally analyzed for the two main prototypes in $d$ -dimensional physics: the hydrogenic and oscillator-like systems.

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Received 7 December 2010

DOI:https://doi.org/10.1103/PhysRevA.83.052107

Authors & Affiliations

Steeve Zozor^1,*, Mariela Portesi^2,†, Pablo Sanchez-Moreno^3,4,‡, and Jesus S. Dehesa^3,5,§

¹Laboratoire Grenoblois d'Image, Parole, Signal et Automatique (GIPSA-Lab, CNRS), 961 rue de la Houille Blanche, F-38402 Saint Martin d'Hères, France
²Instituto de Física La Plata (CONICET), and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata, Argentina
³Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
⁴Departamento de Matemática Aplicada, Universidad de Granada, E-18071 Granada, Spain
⁵Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, E-18071 Granada, Spain

^*steeve.zozor@gipsa-lab.grenoble-inp.fr
^†portesi@fisica.unlp.edu.ar
^‡pablos@ugr.es
^§dehesa@ugr.es

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Issue

Vol. 83, Iss. 5 — May 2011

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