Bound state solutions of the radial Klein-Gordon equation: Application to D- dimensional quantum information theory under exponential-type plus Yukawa potentials

Bound state solutions of the radial Klein-Gordon equation: Application to D- dimensional quantum information theory under exponential-type plus Yukawa potentials | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Bound state solutions of the radial Klein-Gordon equation: Application to D- dimensional quantum information theory under exponential-type plus Yukawa potentials R. Horchani, E. Omugbe, I. J. Njoku, L. M. Pérez, C. A. Onate, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4523621/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted 13 You are reading this latest preprint version Abstract The bound-state solution of the Klein-Gordon equation has been obtained under the interaction of an exponential-type and Yukawa potential functions. The Greene-Aldrich approximation has been used to overcome the centrifugal barrier and enable the analytical solutions of the energy and wave functions in closed form. The D-dimensional momentum space wave function has been constructed using the Fourier transform. The mean values have been conjectured for the position and momentum spaces using two equivalent equations. The effects of the potential parameters on the expectation values and quantum information measurement have been investigated. For the 1D case, the results obey the Heisenberg uncertainty principle, Fisher, Shannon, Onicescu, and the Renyi entropic inequalities. Other information complexities measures, such as Shannon Power, Fisher-Shannon, and Lopez-Ruiz-Mancini-Calbet, have been verified. For the ground state, the 1D momentum expectation value \(\:{⟨{p}^{2}⟩\:}_{00}\) coincides with the 3D \(\:{⟨{p}^{2}⟩\:}_{000}\) values, which is an indication of degeneracy. The total energy of a particle in both 1D and 3D space may be degenerate due to the inter-dimensional degeneracy of the quantum numbers. However, in this present result, the degeneracy in 1D and 3D occurred for fixed quantum states at different momentum intervals. Thus, in 1D, a particle may transit an entire space ( \(\:-\infty\:<p<\infty\:)\) with a certain kinetic energy, which must be equal to its kinetic energy if it moves through the interval \(\:0<p<\infty\:\) in 3D space. This may have implications for kinetic energy degeneracy in higher dimensions. Physical sciences/Physics Physical sciences/Physics/Information theory and computation Physical sciences/Physics/Quantum physics Radial Klein-Gordon equation Shannon entropy Renyi entropy Fisher information kinetic energy Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 19 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 08 Oct, 2024 Reviews received at journal 11 Sep, 2024 Reviewers agreed at journal 12 Aug, 2024 Reviewers agreed at journal 12 Aug, 2024 Reviews received at journal 01 Aug, 2024 Reviews received at journal 24 Jul, 2024 Reviewers agreed at journal 22 Jul, 2024 Reviewers agreed at journal 22 Jul, 2024 Reviewers invited by journal 22 Jul, 2024 Editor assigned by journal 22 Jul, 2024 Editor invited by journal 22 Jul, 2024 Submission checks completed at journal 17 Jul, 2024 First submitted to journal 03 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4523621","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":338416114,"identity":"81511714-4f5b-4f89-b2e2-0178e51a4236","order_by":0,"name":"R. 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The Greene-Aldrich approximation has been used to overcome the centrifugal barrier and enable the analytical solutions of the energy and wave functions in closed form. The D-dimensional momentum space wave function has been constructed using the Fourier transform. The mean values have been conjectured for the position and momentum spaces using two equivalent equations. The effects of the potential parameters on the expectation values and quantum information measurement have been investigated. For the 1D case, the results obey the Heisenberg uncertainty principle, Fisher, Shannon, Onicescu, and the Renyi entropic inequalities. Other information complexities measures, such as Shannon Power, Fisher-Shannon, and Lopez-Ruiz-Mancini-Calbet, have been verified. For the ground state, the 1D momentum expectation value \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\u0026lang;{p}^{2}\u0026rang;\\:}_{00}\\)\u003c/span\u003e\u003c/span\u003e coincides with the 3D \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\u0026lang;{p}^{2}\u0026rang;\\:}_{000}\\)\u003c/span\u003e\u003c/span\u003e values, which is an indication of degeneracy. The total energy of a particle in both 1D and 3D space may be degenerate due to the inter-dimensional degeneracy of the quantum numbers. However, in this present result, the degeneracy in 1D and 3D occurred for fixed quantum states at different momentum intervals. Thus, in 1D, a particle may transit an entire space (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-\\infty\\:\u0026lt;p\u0026lt;\\infty\\:)\\)\u003c/span\u003e\u003c/span\u003e with a certain kinetic energy, which must be equal to its kinetic energy if it moves through the interval \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:0\u0026lt;p\u0026lt;\\infty\\:\\)\u003c/span\u003e\u003c/span\u003e in 3D space. This may have implications for kinetic energy degeneracy in higher dimensions.\u003c/p\u003e","manuscriptTitle":"Bound state solutions of the radial Klein-Gordon equation: Application to D- dimensional quantum information theory under exponential-type plus Yukawa potentials","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-12 18:27:16","doi":"10.21203/rs.3.rs-4523621/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-10-08T05:31:17+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-11T12:18:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"38675901993254741299256139414877874603","date":"2024-08-12T12:10:39+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"42099323619891017076973252235968694801","date":"2024-08-12T11:44:12+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-01T17:40:56+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-24T04:34:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"294566606553400254718065535010503856169","date":"2024-07-22T12:50:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"185982068748802471277710536102766214345","date":"2024-07-22T12:35:00+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-22T11:55:14+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-22T10:22:01+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-07-22T06:22:17+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-17T13:02:26+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-06-03T18:25:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d4c327d6-2ca9-49ed-9be5-93aca3931b27","owner":[],"postedDate":"August 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":35856129,"name":"Physical sciences/Physics"},{"id":35856131,"name":"Physical sciences/Physics/Information theory and computation"},{"id":35856133,"name":"Physical sciences/Physics/Quantum physics"}],"tags":[],"updatedAt":"2024-11-25T16:07:18+00:00","versionOfRecord":{"articleIdentity":"rs-4523621","link":"https://doi.org/10.1038/s41598-024-80123-9","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-11-19 15:57:47","publishedOnDateReadable":"November 19th, 2024"},"versionCreatedAt":"2024-08-12 18:27:16","video":"","vorDoi":"10.1038/s41598-024-80123-9","vorDoiUrl":"https://doi.org/10.1038/s41598-024-80123-9","workflowStages":[]},"version":"v1","identity":"rs-4523621","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4523621","identity":"rs-4523621","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}