Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems

摘要

In this work we find that not only the Heisenberg-like uncertainty productsand the R\'enyi-entropy-based uncertainty sum have the same first-order valuesfor all the quantum states of the $D$-dimensional hydrogenic andoscillator-like systems, respectively, in the pseudoclassical ($D \to \infty$)limit but a similar phenomenon also happens for both theFisher-information-based uncertainty product and the Shannon-entropy-baseduncertainty sum, as well as for the Cr\'amer-Rao and Fisher-Shannoncomplexities. Moreover, we show that the LMC (L\'opez-Ruiz-Mancini-Calvet) andLMC-R\'enyi complexity measures capture the hydrogenic-harmonic difference inthe high dimensional limit already at first order.