{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T09:59:41Z","timestamp":1785146381813,"version":"3.55.0"},"reference-count":101,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T00:00:00Z","timestamp":1780963200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T00:00:00Z","timestamp":1780963200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Universidade Federal Do Cear\u00e1"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In this work, we examine the quantum information characteristics of a hydrogen-like system under a Coulomb potential by using previously derived exact solutions of the generalized Schr\u00f6dinger equation formulated within the conformable fractional framework. The approach introduces a fractional parameter\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$(0 &lt; \\alpha \\le 1)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                            <mml:mo>&lt;<\/mml:mo>\n                            <mml:mi>\u03b1<\/mml:mi>\n                            <mml:mo>\u2264<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , which permits a continuous transition between standard quantum mechanics and a fractional description. Utilizing these available analytical solutions, we determine the associated energy spectrum and wavefunctions and employ them to quantify the informational structure of the system. In particular, we calculate the Shannon entropy in both position and momentum spaces, along with the Fisher information, as fundamental indicators of uncertainty, spatial spreading, and sensitivity to local variations of the probability density. The results show that the fractional parameter\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$(\\alpha )$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mi>\u03b1<\/mml:mi>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    produces nontrivial corrections to these quantum information measures, indicating modifications in localization properties and momentum profiles. Also, the formalism recovers the conventional hydrogenic limit when\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$(\\alpha \\rightarrow 1)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mi>\u03b1<\/mml:mi>\n                            <mml:mo>\u2192<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , which validates the consistency of the formulation. In this context, these results show that the conformable fractional framework constitutes a consistent extension for analyzing quantum systems via information-theoretic quantities without modifying the exact solutions, providing a systematic approach to investigate deviations from integer-order dynamics.\n                  <\/jats:p>","DOI":"10.1007\/s11128-026-05229-7","type":"journal-article","created":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T08:17:49Z","timestamp":1780993069000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantum information measures of conformal fractional non-relativistic systems in a Coulomb potential"],"prefix":"10.1007","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-2724-4822","authenticated-orcid":false,"given":"Quezia R. D. S.","family":"Moreira","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6535-493X","authenticated-orcid":false,"given":"Allan R. P.","family":"Moreira","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3363-980X","authenticated-orcid":false,"given":"Abdelmalek","family":"Bouzenada","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4004-0926","authenticated-orcid":false,"given":"Jo\u00e3o B. R.","family":"Silva","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7603-2904","authenticated-orcid":false,"given":"Ridha","family":"Horchani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2196-9622","authenticated-orcid":false,"given":"Faizuddin","family":"Ahmed","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,9]]},"reference":[{"issue":"8","key":"5229_CR1","doi-asserted-by":"publisher","first-page":"1614","DOI":"10.1103\/PhysRevLett.75.1614","volume":"75","author":"R Rouse","year":"1995","unstructured":"Rouse, R., Han, S., Lukens, J.E.: Observation of resonant tunneling between macroscopically distinct quantum levels. Phys. Rev. Lett. 75(8), 1614 (1995)","journal-title":"Phys. Rev. Lett."},{"key":"5229_CR2","first-page":"453","volume":"136","author":"PAM Dirac","year":"1932","unstructured":"Dirac, P.A.M.: Relativistic quantum mechanics. Proc. R. Soc. A 136, 453 (1932)","journal-title":"Proc. R. Soc. A"},{"key":"5229_CR3","volume-title":"Relativistic Quantum Mechanics","author":"W Greiner","year":"2000","unstructured":"Greiner, W.: Relativistic Quantum Mechanics. Springer-Verlag, Berlin (2000)"},{"key":"5229_CR4","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1103\/RevModPhys.20.367","volume":"20","author":"RP Feynman","year":"1948","unstructured":"Feynman, R.P.: Space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys. 20, 367 (1948)","journal-title":"Rev. Mod. Phys."},{"key":"5229_CR5","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1103\/PhysRev.28.1049","volume":"28","author":"E Schr\u00f6dinger","year":"1926","unstructured":"Schr\u00f6dinger, E.: An undulatory theory of the mechanics of atoms and molecules. Phys. Rev. 28, 1049 (1926)","journal-title":"Phys. Rev."},{"key":"5229_CR6","unstructured":"Landau, L.D., Lifshitz, E.M.: Quantum Mechanics: Non-Relativistic Theory. Course of Theoretical Physics, vol. 3, Pergamon (2013)"},{"key":"5229_CR7","doi-asserted-by":"publisher","first-page":"2450032","DOI":"10.1142\/S0217751X24500325","volume":"39","author":"F Ahmed","year":"2024","unstructured":"Ahmed, F., Bouzenada, A.: Relativistic spin-0 Duffin\u2013Kemmer\u2013Petiau equation in Bonnor\u2013Melvin\u2013Lambda solution. Int. J. Mod. Phys. A 39, 2450032 (2024)","journal-title":"Int. J. Mod. Phys. A"},{"key":"5229_CR8","doi-asserted-by":"publisher","DOI":"10.1088\/1572-9494\/ad2e88","volume":"76","author":"F Ahmed","year":"2024","unstructured":"Ahmed, F., Bouzenada, A.: Study of scalar particles through the Klein\u2013Gordon equation under rainbow gravity effects in Bonnor\u2013Melvin\u2013Lambda space-time. Commun. Theor. Phys. 76, 045401 (2024)","journal-title":"Commun. Theor. Phys."},{"key":"5229_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2024.116490","volume":"1000","author":"F Ahmed","year":"2024","unstructured":"Ahmed, F., Bouzenada, A.: Quantum dynamics of spin-0 particles in a cosmological space-time. Nucl. Phys. B 1000, 116490 (2024)","journal-title":"Nucl. Phys. B"},{"key":"5229_CR10","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ad4830","volume":"99","author":"F Ahmed","year":"2024","unstructured":"Ahmed, F., Bouzenada, A.: Scalar fields in Bonnor\u2013Melvin\u2013Lambda universe with potential: a study of dynamics of spin-zero particles-antiparticles. Phys. Scr. 99, 065033 (2024)","journal-title":"Phys. Scr."},{"issue":"10","key":"5229_CR11","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1140\/epjc\/s10052-024-13437-7","volume":"84","author":"F Ahmed","year":"2024","unstructured":"Ahmed, F., Bouzenada, A.: Effects of gravity rainbow on scalar bosonic and oscillator fields in Bonnor\u2013Melvin space-time with a cosmological constant. Eur. Phys. J. C 84(10), 1045 (2024)","journal-title":"Eur. Phys. J. C"},{"issue":"10","key":"5229_CR12","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1140\/epjp\/s13360-024-05706-x","volume":"139","author":"F Ahmed","year":"2024","unstructured":"Ahmed, F., Bouzenada, A.: Position dependent mass (PDM) Klein\u2013Gordon scalar particles in Bonnor\u2013Melvin\u2013Lambda space-time. Eur. Phys. J. Plus 139(10), 911 (2024)","journal-title":"Eur. Phys. J. Plus"},{"key":"5229_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2024.116682","volume":"1007","author":"A Bouzenada","year":"2024","unstructured":"Bouzenada, A., Boumali, A., Ahmed, F.: Dynamics of spin-0 (particles-antiparticles) in Bonnor\u2013Melvin cosmological space-time using the generalized Feshbach\u2013Villars transformation. Nucl. Phys. B 1007, 116682 (2024)","journal-title":"Nucl. Phys. B"},{"key":"5229_CR14","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1103\/RevModPhys.64.51","volume":"64","author":"CA Mead","year":"1992","unstructured":"Mead, C.A.: The geometric phase in molecular systems. Rev. Mod. Phys. 64, 51 (1992)","journal-title":"Rev. Mod. Phys."},{"key":"5229_CR15","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1140\/epjc\/s10052-016-4241-3","volume":"76","author":"SS Kumar","year":"2016","unstructured":"Kumar, S.S., Shankaranarayanan, S.: Quantum entanglement and Hawking temperature. Eur. Phys. J. C 76, 400 (2016)","journal-title":"Eur. Phys. J. C"},{"key":"5229_CR16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.89.105024","volume":"89","author":"X Busch","year":"2014","unstructured":"Busch, X., Parentani, R.: Quantum entanglement in analogue Hawking radiation: when is the final state nonseparable? Phys. Rev. D 89, 105024 (2014)","journal-title":"Phys. Rev. D"},{"key":"5229_CR17","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1007\/JHEP11(2013)208","volume":"11","author":"L McGough","year":"2013","unstructured":"McGough, L., Verlinde, H.: Bekenstein\u2013Hawking entropy as topological entanglement entropy. J. High Energy Phys. 11, 208 (2013)","journal-title":"J. High Energy Phys."},{"key":"5229_CR18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.103.100402","volume":"103","author":"H Miao","year":"2009","unstructured":"Miao, H., Danilishin, S., Corbitt, T., Chen, Y.: Standard quantum limit for probing mechanical energy quantization. Phys. Rev. Lett. 103, 100402 (2009)","journal-title":"Phys. Rev. Lett."},{"key":"5229_CR19","doi-asserted-by":"publisher","first-page":"42539","DOI":"10.1038\/srep42539","volume":"7","author":"ZX Man","year":"2017","unstructured":"Man, Z.X., Xia, Y.J., An, N.B.: Simultaneous observation of particle and wave behaviors of entangled photons. Sci. Rep. 7, 42539 (2017)","journal-title":"Sci. Rep."},{"key":"5229_CR20","doi-asserted-by":"crossref","unstructured":"Butzer, P., Trebels, W.: Hilberttransformation. Gebrochene Integration und Differentiation. Westdeutscher Verlag, K\u00f6ln und Opladen (1968)","DOI":"10.1007\/978-3-663-07257-7"},{"key":"5229_CR21","doi-asserted-by":"crossref","unstructured":"Ross, B.: Fractional Calculus and its Applications. Lecture Notes in Mathematics, vol. 457. Springer, Berlin (1975)","DOI":"10.1007\/BFb0067095"},{"key":"5229_CR22","unstructured":"Hilfer, R.: In: Scale Invariance and Beyond. Springer, Berlin (1997)"},{"key":"5229_CR23","doi-asserted-by":"crossref","unstructured":"Butzer, P.L., Westphal, U.: In: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)","DOI":"10.1142\/9789812817747_0001"},{"key":"5229_CR24","unstructured":"Nonnenmacher, T.F., Metzler, R.: In: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)"},{"key":"5229_CR25","unstructured":"Schiessel, H., Friedrich, C., Blumen, A.: In: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)"},{"key":"5229_CR26","unstructured":"West, B., Grigolini, P.: In: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)"},{"key":"5229_CR27","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1186\/1687-1847-2012-142","volume":"2012","author":"F Jarad","year":"2012","unstructured":"Jarad, F., Abdeljawad, T., Baleanu, D.: Caputo-type modification of the Hadamard fractional derivatives. Adv. Difference Equ. 2012, 142 (2012)","journal-title":"Adv. Difference Equ."},{"key":"5229_CR28","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1186\/1687-1847-2014-10","volume":"2014","author":"YY Gambo","year":"2014","unstructured":"Gambo, Y.Y., Jarad, F., Baleanu, D., Abdeljawad, T.: On Caputo modification of the Hadamard fractional derivatives. Adv. Difference Equ. 2014, 10 (2014)","journal-title":"Adv. Difference Equ."},{"key":"5229_CR29","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1111\/j.1365-246X.1967.tb02303.x","volume":"13","author":"M Caputo","year":"1967","unstructured":"Caputo, M.: Linear models of dissipation whose $$Q$$ is almost frequency independent 2. Geophys. J. R. Astr. Soc. 13, 529\u2013539 (1967)","journal-title":"Geophys. J. R. Astr. Soc."},{"key":"5229_CR30","volume-title":"Fractional Differential Equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego-London (1999)"},{"key":"5229_CR31","volume-title":"Fractional Integrals and Derivatives","author":"SG Samko","year":"1993","unstructured":"Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives. Gordon and Breach Science Publishers, Yverdon (1993)"},{"key":"5229_CR32","volume-title":"The Fractional Calculus","author":"KB Oldham","year":"1974","unstructured":"Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York-London (1974)"},{"issue":"5","key":"5229_CR33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.66.056108","volume":"66","author":"N Laskin","year":"2002","unstructured":"Laskin, N.: Fractional Schr\u00f6dinger equation. Phys. Rev. E 66(5), 056108 (2002)","journal-title":"Phys. Rev. E"},{"issue":"4\u20136","key":"5229_CR34","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1016\/S0375-9601(00)00201-2","volume":"268","author":"N Laskin","year":"2000","unstructured":"Laskin, N.: Fractional quantum mechanics and L\u00e9vy path integrals. Phys. Lett. A 268(4\u20136), 298\u2013305 (2000)","journal-title":"Phys. Lett. A"},{"issue":"12","key":"5229_CR35","doi-asserted-by":"publisher","first-page":"7113","DOI":"10.3934\/dcds.2019298","volume":"39","author":"D G\u00f3mez-Castro","year":"2019","unstructured":"G\u00f3mez-Castro, D., V\u00e1zquez, J.: The fractional Schr\u00f6dinger equation with singular potential and measure data. Discrete Contin. Dyn. Syst. 39(12), 7113\u20137139 (2019)","journal-title":"Discrete Contin. Dyn. Syst."},{"issue":"1","key":"5229_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0370-1573(00)00070-3","volume":"339","author":"R Metzler","year":"2000","unstructured":"Metzler, R., Klafter, J.: The random walk\u2019s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339(1), 1\u201377 (2000)","journal-title":"Phys. Rep."},{"issue":"4","key":"5229_CR37","doi-asserted-by":"publisher","first-page":"712","DOI":"10.2478\/s13540-012-0048-6","volume":"15","author":"F Mainardi","year":"2012","unstructured":"Mainardi, F.: An historical perspective on fractional calculus in linear viscoelasticity: short survey. Fract. Calc. Appl. Anal. 15(4), 712\u2013717 (2012)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"5229_CR38","doi-asserted-by":"publisher","DOI":"10.1142\/3779","volume-title":"Applications of Fractional Calculus in Physics","author":"R Hilfer","year":"2000","unstructured":"Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)"},{"key":"5229_CR39","doi-asserted-by":"publisher","DOI":"10.1142\/8072","volume-title":"Fractional Calculus: An Introduction for Physicists","author":"R Herrmann","year":"2011","unstructured":"Herrmann, R.: Fractional Calculus: An Introduction for Physicists. World Scientific, Singapore (2011)"},{"key":"5229_CR40","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379 (1948)","journal-title":"Bell Syst. Tech. J."},{"key":"5229_CR41","doi-asserted-by":"publisher","first-page":"B864","DOI":"10.1103\/PhysRev.136.B864","volume":"136","author":"P Hohenberg","year":"1964","unstructured":"Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964)","journal-title":"Phys. Rev."},{"key":"5229_CR42","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-58671-7","volume-title":"Molecular Similarity","author":"KD Sen","year":"1995","unstructured":"Sen, K.D.: Molecular Similarity. Topics in Current Chemistry, Springer, Heidelberg (1995)"},{"key":"5229_CR43","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1002\/ijch.198000018","volume":"19","author":"SB Sears","year":"1980","unstructured":"Sears, S.B., Parr, R.G., Dinur, U.: On the quantum-mechanical kinetic energy as a measure of the information in a distribution. Israel J. Chem. 19, 165 (1980)","journal-title":"Israel J. Chem."},{"key":"5229_CR44","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511622670","volume-title":"Physics from the Fisher Information: A Unification","author":"BR Frieden","year":"1998","unstructured":"Frieden, B.R.: Physics from the Fisher Information: A Unification. Cambridge University Press, Cambridge (1998)"},{"key":"5229_CR45","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1017\/S0305004100009580","volume":"22","author":"RA Fisher","year":"1925","unstructured":"Fisher, R.A.: Theory of statistical estimation. Proc. Camb. Philos. Soc. 22, 700 (1925)","journal-title":"Proc. Camb. Philos. Soc."},{"key":"5229_CR46","doi-asserted-by":"publisher","first-page":"3832","DOI":"10.1016\/j.ins.2009.07.013","volume":"179","author":"JF Bercher","year":"2009","unstructured":"Bercher, J.F., Vignat, C.: On minimum Fisher information distributions with restricted support and fixed variance. Inf. Sci. 179, 3832 (2009)","journal-title":"Inf. Sci."},{"key":"5229_CR47","doi-asserted-by":"crossref","unstructured":"Wilson, M.: Nanotechnology. Basic Science and Emerging Technologies. CRC Press, New York (2003)","DOI":"10.1201\/9781420035230"},{"key":"5229_CR48","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2001","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2001)"},{"key":"5229_CR49","unstructured":"Lopez-Rosa, S.: Information-Theoretic Measures of Atomic and Molecular Systems. Spain. Ph.D. Thesis, (2010)."},{"key":"5229_CR50","doi-asserted-by":"publisher","first-page":"1529","DOI":"10.1002\/qua.22244","volume":"110","author":"JS Dehesa","year":"2010","unstructured":"Dehesa, J.S., Lopez-Rosa, S., Mart\u00ednez-Finkelshtein, A., Y\u00e1\u00f1ez, R.J.: Information theory of D-dimensional hydrogenic systems: application to circular and Rydberg states. Int. J. Quantum Chem. 110, 1529 (2010)","journal-title":"Int. J. Quantum Chem."},{"key":"5229_CR51","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/25\/4\/040301","volume":"25","author":"SA Najafizade","year":"2016","unstructured":"Najafizade, S.A., Hassanabadi, H., Zarrinkamar, S.: Nonrelativistic Shannon information entropy for Kratzer potential. Chin. Phys. B 25, 040301 (2016)","journal-title":"Chin. Phys. B"},{"key":"5229_CR52","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1140\/epjp\/s13360-020-00525-2","volume":"135","author":"AN Ikot","year":"2020","unstructured":"Ikot, A.N., Rampho, G.J., Amadi, P.O., Sithole, M.J., Okorie, U.S., Lekala, M.I.: Shannon entropy and Fisher information-theoretic measures for Mobius square potential. Eur. Phys. J. Plus 135, 6 (2020)","journal-title":"Eur. Phys. J. Plus"},{"key":"5229_CR53","doi-asserted-by":"publisher","DOI":"10.1002\/qua.25620","volume":"118","author":"CN Isonguyo","year":"2018","unstructured":"Isonguyo, C.N., Oyewumi, K.J., Oyun, O.S.: Quantum information-theoretic measures for the static screened Coulomb potential. Int. J. Quantum Chem. 118, e25620 (2018)","journal-title":"Int. J. Quantum Chem."},{"key":"5229_CR54","doi-asserted-by":"publisher","first-page":"934","DOI":"10.1002\/andp.201300089","volume":"525","author":"GH Sun","year":"2013","unstructured":"Sun, G.H., Dong, S.H., Saad, N.: Quantum information entropies for an asymmetric trigonometric Rosen\u2013Morse potential. Ann. Phys. 525, 934 (2013)","journal-title":"Ann. Phys."},{"key":"5229_CR55","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/j.physleta.2013.11.020","volume":"378","author":"S Dong","year":"2014","unstructured":"Dong, S., Sun, G.H., Dong, S.H., Draayer, J.P.: Quantum information entropies for a squared tangent potential well. Phys. Lett. A 378, 124 (2014)","journal-title":"Phys. Lett. A"},{"key":"5229_CR56","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1002\/qua.24928","volume":"115","author":"GH Sun","year":"2015","unstructured":"Sun, G.H., Dong, S.H., Launey, K.D., Dytrych, T., Draayer, J.P.: Shannon information entropy for a hyperbolic double-well potential. Int. J. Quantum Chem. 115, 891 (2015)","journal-title":"Int. J. Quantum Chem."},{"key":"5229_CR57","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1140\/epjd\/s10053-022-00395-6","volume":"76","author":"E Omugbe","year":"2022","unstructured":"Omugbe, E., Osafile, O.E., Okon, I.B., Eyube, E.S., Inyang, E.P., Okorie, U.S., Jahanshir, A., Onate, C.A.: Non-relativistic bound state solutions with $$\\alpha $$-deformed Kratzer-type potential using the super-symmetric WKB method: application to theoretic-information measures. Eur. Phys. J. D 76, 72 (2022)","journal-title":"Eur. Phys. J. D"},{"key":"5229_CR58","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1007\/BF01397280","volume":"43","author":"W Heisenberg","year":"1927","unstructured":"Heisenberg, W.: \u00dcber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172 (1927)","journal-title":"Z. Phys."},{"issue":"5","key":"5229_CR59","doi-asserted-by":"publisher","first-page":"976","DOI":"10.3390\/sym14050976","volume":"14","author":"CO Edet","year":"2022","unstructured":"Edet, C.O., Ettah, E.B., Aljunid, S.A., Endut, R., Ali, N., Ikot, A.N., Asjad, M.: Global quantum information-theoretic measures in the presence of magnetic and Aharonov\u2013Bohm fields. Symmetry 14(5), 976 (2022)","journal-title":"Symmetry"},{"key":"5229_CR60","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF01608825","volume":"44","author":"I Bialynicki-Birula","year":"1975","unstructured":"Bialynicki-Birula, I., Mycielski, J.: Uncertainty relations for information entropy in wave mechanics. Commun. Math. Phys. 44, 129 (1975)","journal-title":"Commun. Math. Phys."},{"key":"5229_CR61","doi-asserted-by":"publisher","first-page":"25368","DOI":"10.1002\/qua.25368","volume":"117","author":"R Pooja","year":"2017","unstructured":"Pooja, R., Sharma, A., Gupta, R., Kumar, A.: Quantum information entropy of modified Hylleraas plus exponential Rosen\u2013Morse potential and squeezed states. Int. J. Quantum Chem. 117, 25368 (2017)","journal-title":"Int. J. Quantum Chem."},{"key":"5229_CR62","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.1002\/qua.25197","volume":"116","author":"R Pooja","year":"2016","unstructured":"Pooja, R., Kumar, R., Kumar, G., Kumar, R., Kumar, A.: Quantum information entropy of Eckart potential. Int. J. Quantum Chem. 116, 1413 (2016)","journal-title":"Int. J. Quantum Chem."},{"issue":"7","key":"5229_CR63","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ad56df","volume":"99","author":"F Ahmed","year":"2024","unstructured":"Ahmed, F., Bouzenada, A., Moreira, A.R.: Effects of P\u00f6schl-Teller potential on approximate $$\\ell \\ne 0$$-states solution in topological defect geometry and Shannon entropy. Phys. Scr. 99(7), 075411 (2024)","journal-title":"Phys. Scr."},{"issue":"3","key":"5229_CR64","doi-asserted-by":"publisher","DOI":"10.1080\/00268976.2024.2365420","volume":"123","author":"F Ahmed","year":"2025","unstructured":"Ahmed, F., Bouzenada, A., Moreira, A.R.: Global monopole effects on exact s-state solution under trigonometric P\u00f6schl-Teller potential. Mol. Phys. 123(3), e2365420 (2025)","journal-title":"Mol. Phys."},{"key":"5229_CR65","doi-asserted-by":"publisher","first-page":"3163","DOI":"10.1007\/s12648-025-03563-7","volume":"99","author":"ARP Moreira","year":"2025","unstructured":"Moreira, A.R.P., Bouzenada, A., Ahmed, F.: Measures of quantum information for a graphene Dirac electron under the influence of magnetic fields. Indian J. Phys. 99, 3163\u20133172 (2025)","journal-title":"Indian J. Phys."},{"issue":"6","key":"5229_CR66","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/s10825-025-02422-2","volume":"24","author":"ARP Moreira","year":"2025","unstructured":"Moreira, A.R.P., Bouzenada, A., Ahmed, F.: Quantum information measurements of the exact solution of the Schr\u00f6dinger equation for a q-deformed Morse potential. J. Comput. Electron. 24(6), 185 (2025)","journal-title":"J. Comput. Electron."},{"issue":"23","key":"5229_CR67","doi-asserted-by":"publisher","first-page":"2550088","DOI":"10.1142\/S0217751X25500885","volume":"40","author":"AR Moreira","year":"2025","unstructured":"Moreira, A.R., Ma, L., Bouzenada, A., Ahmed, F.: Shannon entropy of fermions in G\u00f6del-type space-times with torsion and topological defects. Int. J. Mod. Phys. A 40(23), 2550088 (2025)","journal-title":"Int. J. Mod. Phys. A"},{"issue":"12","key":"5229_CR68","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ad92be","volume":"99","author":"ARP Moreira","year":"2024","unstructured":"Moreira, A.R.P., Bouzenada, A., Ahmed, F.: Quantum information for graphene wormholes. Phys. Scr. 99(12), 125121 (2024)","journal-title":"Phys. Scr."},{"key":"5229_CR69","doi-asserted-by":"crossref","unstructured":"Moreira, A.R.P., Bouzenada, A., Abdi, M., Ahmed, F., Ikot, A.N.: Quantum information in G\u00f6del-type geometries with conical topology for spin-1\/2 particles. Int. J. Geom. Methods Mod. Phys. (2025)","DOI":"10.1142\/S0219887826500556"},{"issue":"10","key":"5229_CR70","doi-asserted-by":"publisher","first-page":"760","DOI":"10.1007\/s00339-025-08905-0","volume":"131","author":"ARP Moreira","year":"2025","unstructured":"Moreira, A.R.P., Bouzenada, A., Abdi, M., Ahmed, F.: Effects of magnetic flux on the information entropy of graphene magnetic quantum dots. Appl. Phys. A 131(10), 760 (2025)","journal-title":"Appl. Phys. A"},{"issue":"08","key":"5229_CR71","doi-asserted-by":"publisher","first-page":"2550217","DOI":"10.1142\/S0219887825502172","volume":"23","author":"ARP Moreira","year":"2026","unstructured":"Moreira, A.R.P., Bouzenada, A., Ahmed, F.: Impact of complex magnetic fields on quantum information in graphene. Int. J. Geom. Methods Mod. Phys. 23(08), 2550217 (2026)","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"issue":"3","key":"5229_CR72","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s10909-025-03282-7","volume":"219","author":"F Ahmed","year":"2025","unstructured":"Ahmed, F., Bouzenada, A., Moreira, A.R.: Effects of Conical Geometry on Approximate Solutions Under Modified P\u00f6schl-Teller Potential and Shannon Entropy. J. Low Temp. Phys. 219(3), 87\u2013102 (2025)","journal-title":"J. Low Temp. Phys."},{"key":"5229_CR73","doi-asserted-by":"publisher","first-page":"2463","DOI":"10.1007\/s10773-010-0432-0","volume":"49","author":"WF Liu","year":"2010","unstructured":"Liu, W.F., Zhang, L.H., Li, C.J.: Quantum Fisher information in two-qubit pure states. Int. J. Theor. Phys. 49, 2463\u20132475 (2010)","journal-title":"Int. J. Theor. Phys."},{"key":"5229_CR74","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1007\/s11082-019-2185-1","volume":"52","author":"F Ozaydin","year":"2020","unstructured":"Ozaydin, F., Altintas, A.A.: Parameter estimation with Dzyaloshinskii\u2013Moriya interaction under external magnetic fields. Opt. Quantum Electron. 52, 70 (2020)","journal-title":"Opt. Quantum Electron."},{"issue":"1","key":"5229_CR75","doi-asserted-by":"publisher","first-page":"137","DOI":"10.18576\/pfda\/100113","volume":"10","author":"MG Al-Masaeed","year":"2024","unstructured":"Al-Masaeed, M.G., Rabei, E.M., Al-Jamel, A.: Analytical solution of conformable Schr\u00f6dinger wave equation with Coulomb potential. Progr. Fract. Differ. Appl. 10(1), 137\u2013153 (2024)","journal-title":"Progr. Fract. Differ. Appl."},{"key":"5229_CR76","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/accda1","volume":"98","author":"XH Wang","year":"2023","unstructured":"Wang, X.H., Chen, C.Y., You, Y., Sun, D.S., Lu, F.L., Dong, S.H.: Exact solutions of the Schr\u00f6dinger equation for another class of hyperbolic potential wells. Phys. Scr. 98, 055404 (2023)","journal-title":"Phys. Scr."},{"key":"5229_CR77","doi-asserted-by":"publisher","first-page":"1516","DOI":"10.3390\/e24111516","volume":"24","author":"R Santana-Carrillo","year":"2022","unstructured":"Santana-Carrillo, R., Gonz\u00e1lez-Flores, J.S., Maga\u00f1a-Espinal, E., Quezada, L.F., Sun, G.H., Dong, S.H.: Quantum information entropy of hyperbolic potentials in fractional Schr\u00f6dinger equation. Entropy 24, 1516 (2022)","journal-title":"Entropy"},{"key":"5229_CR78","doi-asserted-by":"publisher","first-page":"604","DOI":"10.3390\/e24050604","volume":"24","author":"CA Gil-Barrera","year":"2022","unstructured":"Gil-Barrera, C.A., Santana-Carrillo, R., Sun, G.H., Dong, S.H.: Quantum information entropies on hyperbolic single potential wells. Entropy 24, 604 (2022)","journal-title":"Entropy"},{"key":"5229_CR79","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/acd309","volume":"98","author":"FCE Lima","year":"2023","unstructured":"Lima, F.C.E., Moreira, A.R.P., Almeida, C.A.S., Edet, C.O., Ali, N.: Quantum information entropy of a particle trapped by the Aharonov\u2013Bohm-type effect. Phys. Scr. 98, 065111 (2023)","journal-title":"Phys. Scr."},{"key":"5229_CR80","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s10825-021-01840-2","volume":"21","author":"ARP Moreira","year":"2022","unstructured":"Moreira, A.R.P.: Quantum information for a solitonic particle with hyperbolic interaction. J. Comput. Electron. 21, 21 (2022)","journal-title":"J. Comput. Electron."},{"key":"5229_CR81","doi-asserted-by":"publisher","DOI":"10.1002\/qua.26645","volume":"121","author":"FCE Lima","year":"2021","unstructured":"Lima, F.C.E., Moreira, A.R.P., Almeida, C.A.S.: Information and thermodynamic properties of a non-Hermitian particle ensemble. Int. J. Quantum Chem. 121, e26645 (2021)","journal-title":"Int. J. Quantum Chem."},{"key":"5229_CR82","doi-asserted-by":"publisher","DOI":"10.1002\/qua.26749","volume":"121","author":"FCE Lima","year":"2021","unstructured":"Lima, F.C.E., Moreira, A.R.P., Almeida, C.A.S.: Statistical properties of linear Majorana fermions. Int. J. Quantum Chem. 121, e26749 (2021)","journal-title":"Int. J. Quantum Chem."},{"key":"5229_CR83","doi-asserted-by":"publisher","DOI":"10.1016\/j.physe.2023.115747","volume":"152","author":"ARP Moreira","year":"2023","unstructured":"Moreira, A.R.P.: Thermodynamic properties and entropy information of fermions in the Rindler spacetime. Phys. E. Low Dimens. Syst. Nanostruct. 152, 115747 (2023)","journal-title":"Phys. E. Low Dimens. Syst. Nanostruct."},{"key":"5229_CR84","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.aop.2014.05.018","volume":"348","author":"G Y\u00e1\u00f1ez-Navarro","year":"2014","unstructured":"Y\u00e1\u00f1ez-Navarro, G., Sun, G.H., Dytrych, T., Launey, K.D., Dong, S.H., Draayer, J.P.: Quantum information entropies for position-dependent mass Schr\u00f6dinger problem. Ann. Phys. 348, 153 (2014)","journal-title":"Ann. Phys."},{"key":"5229_CR85","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1140\/epjc\/s10052-023-12224-0","volume":"83","author":"ARP Moreira","year":"2023","unstructured":"Moreira, A.R.P., Dong, S.H.: Probability measures of fermions on branes. Eur. Phys. J. C 83, 1064 (2023)","journal-title":"Eur. Phys. J. C"},{"key":"5229_CR86","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1016\/j.cjph.2024.03.028","volume":"89","author":"ARP Moreira","year":"2024","unstructured":"Moreira, A.R.P., Amadi, P.O., Horchani, R., Ikot, A.N., Ahmed, F.: The influence of a magnetic field on Shannon entropy and thermal properties in graphene. Chin. J. Phys. 89, 366 (2024)","journal-title":"Chin. J. Phys."},{"key":"5229_CR87","doi-asserted-by":"publisher","first-page":"159","DOI":"10.2307\/1970980","volume":"102","author":"W Beckner","year":"1975","unstructured":"Beckner, W.: Inequalities in Fourier analysis. Ann. Math. 102, 159 (1975)","journal-title":"Ann. Math."},{"key":"5229_CR88","doi-asserted-by":"publisher","first-page":"2230","DOI":"10.1002\/qua.21752","volume":"108","author":"RF Nalewajski","year":"2008","unstructured":"Nalewajski, R.F.: Use of Fisher information in quantum chemistry. Int. J. Quantum Chem. 108, 2230 (2008)","journal-title":"Int. J. Quantum Chem."},{"key":"5229_CR89","doi-asserted-by":"crossref","unstructured":"Nagaoka, H. In: Asymptotic Theory of Quantum Statistical Inference: Selected Papers, p. 113 (2005)","DOI":"10.1142\/9789812563071_0010"},{"key":"5229_CR90","doi-asserted-by":"publisher","DOI":"10.1088\/1572-9494\/ac01e4","volume":"73","author":"YJ Lian","year":"2021","unstructured":"Lian, Y.J., Liu, J.M.: Quantum Fisher information of a qubit-qutrit system in Garfinkle\u2013Horowitz\u2013Strominger dilation space-time. Commun. Theor. Phys. 73, 085102 (2021)","journal-title":"Commun. Theor. Phys."},{"key":"5229_CR91","doi-asserted-by":"publisher","DOI":"10.1088\/1555-6611\/abbed9","volume":"30","author":"BJ Falaye","year":"2020","unstructured":"Falaye, B.J., Liman, M.S.: Probing quantum Fisher information of an open Dirac system with Hawking effect in the Schwarzschild black hole. Laser Phys. 30, 225206 (2020)","journal-title":"Laser Phys."},{"key":"5229_CR92","doi-asserted-by":"publisher","first-page":"1297","DOI":"10.1080\/09500348814551451","volume":"35","author":"BR Frieden","year":"1988","unstructured":"Frieden, B.R.: Applications to optics and wave mechanics of the criterion of maximum Cram\u00e9r-Rao bound. J. Mod. Opt. 35, 1297 (1988)","journal-title":"J. Mod. Opt."},{"key":"5229_CR93","volume-title":"Statistical Mechanics","author":"RK Pathria","year":"1996","unstructured":"Pathria, R.K., Beale, P.D.: Statistical Mechanics, 2nd edn. Butterworth-Heinemann, Oxford (1996)","edition":"2"},{"key":"5229_CR94","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1126\/science.122.3172.675","volume":"122","author":"M Born","year":"1955","unstructured":"Born, M.: Statistical interpretation of quantum mechanics. Science 122, 675 (1955)","journal-title":"Science"},{"key":"5229_CR95","doi-asserted-by":"publisher","first-page":"152","DOI":"10.2307\/2372390","volume":"79","author":"II Hirschmann Jr","year":"1957","unstructured":"Hirschmann, I.I., Jr.: A note on entropy. Amer. J. Math. 79, 152 (1957)","journal-title":"Amer. J. Math."},{"key":"5229_CR96","doi-asserted-by":"publisher","DOI":"10.1088\/0031-8949\/87\/04\/045003","volume":"87","author":"GH Sun","year":"2013","unstructured":"Sun, G.H., Dong, S.H.: Quantum information entropies of the eigenstates for a symmetrically trigonometric Rosen-Morse potential. Phys. Scr. 87, 045003 (2013)","journal-title":"Phys. Scr."},{"key":"5229_CR97","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/22\/5\/050302","volume":"22","author":"GH Sun","year":"2013","unstructured":"Sun, G.H., Aoki, M.A., Dong, S.H.: Quantum information entropies of the eigenstates for the P\u00f6schl-Teller-like potential. Chin. Phys. B 22, 050302 (2013)","journal-title":"Chin. Phys. B"},{"key":"5229_CR98","doi-asserted-by":"publisher","first-page":"1775","DOI":"10.1103\/PhysRevA.58.1775","volume":"58","author":"M Reginatto","year":"1998","unstructured":"Reginatto, M.: Derivation of the equations of nonrelativistic quantum mechanics using the principle of minimum Fisher information. Phys. Rev. A 58, 1775 (1998)","journal-title":"Phys. Rev. A"},{"key":"5229_CR99","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/S0009-2614(03)00335-X","volume":"372","author":"RF Nalewajski","year":"2003","unstructured":"Nalewajski, R.F.: Information principles in the theory of electronic structure. Chem. Phys. Lett. 372, 28 (2003)","journal-title":"Chem. Phys. Lett."},{"key":"5229_CR100","doi-asserted-by":"crossref","unstructured":"Cohen-Tannoudji, C., Diu, B., Lalo\u00eb, F.: Quantum Mechanics Volume I: Basic Concepts, Tools, and Applications, 2nd ed. John Wiley & Sons, Hoboken (2019)","DOI":"10.1515\/9783110638769"},{"key":"5229_CR101","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/j.physleta.2015.09.029","volume":"380","author":"BJ Falaye","year":"2016","unstructured":"Falaye, B.J., Serrano, F.A., Dong, S.H.: Fisher information for the position-dependent mass Schr\u00f6dinger system. Phys. Lett. A 380, 267 (2016)","journal-title":"Phys. Lett. A"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05229-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-026-05229-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05229-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T09:02:37Z","timestamp":1785142957000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-026-05229-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,9]]},"references-count":101,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["5229"],"URL":"https:\/\/doi.org\/10.1007\/s11128-026-05229-7","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,9]]},"assertion":[{"value":"3 March 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no conflict of interest.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"213"}}