High Dimensional Atomic States of Hydrogenic Type: Heisenberg-like and Entropic Uncertainty Measures

High dimensional atomic states play a relevant role in a broad range of quantum fields, ranging from atomic and molecular physics to quantum technologies. The D-dimensional hydrogenic system (i.e., a negatively-charged particle moving around a positively charged core under a Coulomb-like potential)...

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Published inEntropy (Basel, Switzerland) Vol. 23; no. 10; p. 1339
Main Author Dehesa, Jesús S.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 14.10.2021
MDPI
Subjects
Atomic states
Charged particles
Entropy (Information theory)
Heisenberg-like uncertainty measures
high dimensional hydrogenic systems
Molecular physics
Polynomials
Review
Rényi entropies
Shannon entropies
Uncertainty
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Summary:High dimensional atomic states play a relevant role in a broad range of quantum fields, ranging from atomic and molecular physics to quantum technologies. The D-dimensional hydrogenic system (i.e., a negatively-charged particle moving around a positively charged core under a Coulomb-like potential) is the main prototype of the physics of multidimensional quantum systems. In this work, we review the leading terms of the Heisenberg-like (radial expectation values) and entropy-like (Rényi, Shannon) uncertainty measures of this system at the limit of high D. They are given in a simple compact way in terms of the space dimensionality, the Coulomb strength and the state’s hyperquantum numbers. The associated multidimensional position–momentum uncertainty relations are also revised and compared with those of other relevant systems.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e23101339