Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems
In this work we find that not only the Heisenberg-like uncertainty products and the Rényi-entropy-based uncertainty sum have the same first-order values for all the quantum states of the $D$-dimensional hydrogenic and oscillator-like systems, respectively, in the pseudoclassical ($D \to \infty$) limit but a similar phenomenon also happens for both the Fisher-information-based uncertainty product and the Shannon-entropy-based uncertainty sum, as well as for the Crámer-Rao and Fisher-Shannon complexities. Moreover, we show that the LMC (López-Ruiz-Mancini-Calvet) and LMC-Rényi complexity measures capture the hydrogenic-harmonic difference in the high dimensional limit already at first order.
quant-ph↗