@misc{10481/49123,
year = {2017},
month = {4},
url = {http://hdl.handle.net/10481/49123},
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.},
organization = {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},
keywords = {D-dimensional harmonic oscillator},
keywords = {D-dimensional quantum physics},
keywords = {Radial and momentum expectation values},
keywords = {Harmonic states at large dimensions},
title = {Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems},
doi = {10.3390/e19040164},
author = {Puertas-Centeno, David and Valero Toranzo, Irene and Sánchez-Dehesa Moreno-Cid, Jesús},
}