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arXiv · 1708.07299

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

N. Sobrino-Coll·D. Puertas-Centeno·I. V. Toranzo·J. S. Dehesa
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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 $D$-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 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.

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N. Sobrino-Coll, D. Puertas-Centeno, I. V. Toranzo, J. S. Dehesa. 2017-08-24. Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems. https://doi.org/10.1088/1742-5468/aa7df4

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