{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T06:43:01Z","timestamp":1774420981552,"version":"3.50.1"},"reference-count":56,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T00:00:00Z","timestamp":1666569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Mexico","award":["20220355-SIP-IPN"],"award-info":[{"award-number":["20220355-SIP-IPN"]}]},{"name":"Mexico","award":["20220865-SIP-IPN"],"award-info":[{"award-number":["20220865-SIP-IPN"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work we have studied the Shannon information entropy for two hyperbolic single-well potentials in the fractional Schr\u00f6dinger equation (the fractional derivative number (0&lt;n\u22642) by calculating position and momentum entropy. We find that the wave function will move towards the origin as the fractional derivative number n decreases and the position entropy density becomes more severely localized in more fractional system, i.e., for smaller values of n, but the momentum probability density becomes more delocalized. And then we study the Beckner Bialynicki-Birula\u2013Mycieslki (BBM) inequality and notice that the Shannon entropies still satisfy this inequality for different depth u even though this inequality decreases (or increases) gradually as the depth u of the hyperbolic potential U1 (or U2) increases. Finally, we also carry out the Fisher entropy and observe that the Fisher entropy increases as the depth u of the potential wells increases, while the fractional derivative number n decreases.<\/jats:p>","DOI":"10.3390\/e24111516","type":"journal-article","created":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T08:19:06Z","timestamp":1666599546000},"page":"1516","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Quantum Information Entropy of Hyperbolic Potentials in Fractional Schr\u00f6dinger Equation"],"prefix":"10.3390","volume":"24","author":[{"given":"R.","family":"Santana-Carrillo","sequence":"first","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, UPALM, Ciudad de Mexico 07738, Mexico"}]},{"given":"Jesus S.","family":"Gonz\u00e1lez-Flores","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, UPALM, Ciudad de Mexico 07738, Mexico"}]},{"given":"Emilio","family":"Maga\u00f1a-Espinal","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, UPALM, Ciudad de Mexico 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7516-0584","authenticated-orcid":false,"given":"Luis F.","family":"Quezada","sequence":"additional","affiliation":[{"name":"Research Center for Quantum Physics, Huzhou University, Huzhou 313000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0689-2754","authenticated-orcid":false,"given":"Guo-Hua","family":"Sun","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, UPALM, Ciudad de Mexico 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0769-635X","authenticated-orcid":false,"given":"Shi-Hai","family":"Dong","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, UPALM, Ciudad de Mexico 07738, Mexico"},{"name":"Research Center for Quantum Physics, Huzhou University, Huzhou 313000, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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