{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T12:39:44Z","timestamp":1775047184659,"version":"3.50.1"},"reference-count":177,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,14]],"date-time":"2021-05-14T00:00:00Z","timestamp":1620950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The spreading of the stationary states of the multidimensional single-particle systems with a central potential is quantified by means of Heisenberg-like measures (radial and logarithmic expectation values) and entropy-like quantities (Fisher, Shannon, R\u00e9nyi) of position and momentum probability densities. Since the potential is assumed to be analytically unknown, these dispersion and information-theoretical measures are given by means of inequality-type relations which are explicitly shown to depend on dimensionality and state\u2019s angular hyperquantum numbers. The spherical-symmetry and spin effects on these spreading properties are obtained by use of various integral inequalities (Daubechies\u2013Thakkar, Lieb\u2013Thirring, Redheffer\u2013Weyl, ...) and a variational approach based on the extremization of entropy-like measures. Emphasis is placed on the uncertainty relations, upon which the essential reason of the probabilistic theory of quantum systems relies.<\/jats:p>","DOI":"10.3390\/e23050607","type":"journal-article","created":{"date-parts":[[2021,5,14]],"date-time":"2021-05-14T10:54:22Z","timestamp":1620989662000},"page":"607","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4397-9426","authenticated-orcid":false,"given":"Jes\u00fas S.","family":"Dehesa","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain"},{"name":"Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, 18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,14]]},"reference":[{"key":"ref_1","first-page":"60","article-title":"The relation between the properties and atomic weights of the elements","volume":"1","author":"Mendeleev","year":"1869","journal-title":"J. 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