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Entropy 2017, 19(4), 164; doi:10.3390/e19040164

Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems

1
Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain
2
Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editors: Mariela Portesi, Alejandro Hnilo and Federico Holik
Received: 8 March 2017 / Revised: 30 March 2017 / Accepted: 6 April 2017 / Published: 9 April 2017
(This article belongs to the Special Issue Foundations of Quantum Mechanics)
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Abstract

The D-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work, we rigorously determine the leading term of the Heisenberg-like and entropy-like uncertainty measures of this system as given by the radial expectation values and the Rényi entropies, respectively, at the limit of large D. The associated multidimensional position-momentum uncertainty relations are discussed, showing that they saturate the corresponding general ones. A conjecture about the Shannon-like uncertainty relation is given, and an interesting phenomenon is observed: the Heisenberg-like and Rényi-entropy-based equality-type uncertainty relations for all of the D-dimensional harmonic oscillator states in the pseudoclassical ( D ) limit are the same as the corresponding ones for the hydrogenic systems, despite the so different character of the oscillator and Coulomb potentials. View Full-Text
Keywords: entropic uncertainty measures; D-dimensional harmonic oscillator; D-dimensional quantum physics; radial and momentum expectation values; harmonic states at large dimensions entropic uncertainty measures; D-dimensional harmonic oscillator; D-dimensional quantum physics; radial and momentum expectation values; harmonic states at large dimensions
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. (CC BY 4.0).

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Puertas-Centeno, D.; Toranzo, I.V.; Dehesa, J.S. Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems. Entropy 2017, 19, 164.

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