Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems Puertas-Centeno, David Valero Toranzo, Irene Sánchez-Dehesa Moreno-Cid, Jesús Entropic uncertainty measures D-dimensional harmonic oscillator D-dimensional quantum physics Radial and momentum expectation values Harmonic states at large dimensions 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. 2018-01-23T13:14:35Z 2018-01-23T13:14:35Z 2017-04-09 info:eu-repo/semantics/article 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] 1099-4300 http://hdl.handle.net/10481/49123 10.3390/e19040164 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License MDPI