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Advances in Mathematical Physics - Volume 2015 2015, Article ID 120698, 4 pages -

Research Article

Instituto de Física La Plata IFLP-CONICET and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, No. 115 and No. 49, C.C. 67, 1900 La Plata, Argentina

CeBio y Secretaria de Investigacion, Universidad Nacional del Noroeste de la Provincia de Buenos Aires-UNNOBA and CONICET, Roque Saenz Pena 456, Junin, Argentina

Received 10 December 2014; Revised 23 January 2015; Accepted 23 January 2015

Academic Editor: Xiao-Jun Yang

Copyright © 2015 Angelo Plastino et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fisher’s information measure plays a very important role in diverse areas of theoretical physics. The associated measures and , as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product has been conjectured to exhibit a nontrivial lower bound in Hall 2000. More explicitly, this conjecture says that for any pure state of a particle in one dimension . We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schrödinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schrödinger equation. We also conjecture that any normalizable time-dependent solution of this equation verifies for .





Autor: Angelo Plastino, Guido Bellomo, and Angel Ricardo Plastino

Fuente: https://www.hindawi.com/



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