Puertas-Centeno, D.Toranzo, I. V.Dehesa, J. S.2024-10-142024-10-142017-04-09Entropy 2017, 19, 1641099-4300https://hdl.handle.net/10115/40181The 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.engAttribution 4.0 Internationalhttps://creativecommons.org/licenses/by/4.0/Entropic uncertainty measuresD-dimensional harmonic oscillatorD-dimensional quantum physicsRadial and momentum expectation valuesHarmonic states at large dimensionsinfo:eu-repo/semantics/article10.3390/e19040164info:eu-repo/semantics/openAccess