Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems
Quantum Physics
2017-09-13 v1
Abstract
In this work we find that not only the Heisenberg-like uncertainty products and the R\'enyi-entropy-based uncertainty sum have the same first-order values for all the quantum states of the -dimensional hydrogenic and oscillator-like systems, respectively, in the pseudoclassical () 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 Cr\'amer-Rao and Fisher-Shannon complexities. Moreover, we show that the LMC (L\'opez-Ruiz-Mancini-Calvet) and LMC-R\'enyi complexity measures capture the hydrogenic-harmonic difference in the high dimensional limit already at first order.
Keywords
Cite
@article{arxiv.1708.07299,
title = {Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems},
author = {N. Sobrino-Coll and D. Puertas-Centeno and I. V. Toranzo and J. S. Dehesa},
journal= {arXiv preprint arXiv:1708.07299},
year = {2017}
}