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Please use this identifier to cite or link to this item: http://hdl.handle.net/10481/49123

Title: Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
Authors: Puertas-Centeno, David
Valero Toranzo, Irene
Sánchez-Dehesa Moreno-Cid, Jesús
Issue Date: 9-Apr-2017
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.
Sponsorship: This work has been partially supported by the projects FQM-7276 and FQM-207 of the Junta de Andalucía and the MINECO (Ministerio de Economia y Competitividad)-FEDER (European Regional Development Fund) Grants FIS2014- 54497P and FIS2014-59311-P. Irene V. Toranzo acknowledges the support of MEunder the program FPU.
Publisher: MDPI
Keywords: Entropic uncertainty measures
D-dimensional harmonic oscillator
D-dimensional quantum physics
Radial and momentum expectation values
Harmonic states at large dimensions
URI: http://hdl.handle.net/10481/49123
ISSN: 1099-4300
Rights : Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License
Citation: Puertas-Centeno, D.; Valero Toranzo, I.; Sánchez-Dehesa Moreno-Cid, J. Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems. Entropy, 19(4): 164 (2017). [http://hdl.handle.net/10481/49123]
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