Completeness of the Klein-Gordon oscillator eigenfunctions via Hermite and Laguerre polynomials
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Quantum Physics arXiv:2605.21791 (quant-ph) [Submitted on 20 May 2026] Title:Completeness of the Klein-Gordon oscillator eigenfunctions via Hermite and Laguerre polynomials Authors:Kevin Hernández View a PDF of the paper titled Completeness of the Klein-Gordon oscillator eigenfunctions via Hermite and Laguerre polynomials, by Kevin Hern\'andez View PDF HTML (experimental) Abstract:Completeness of the Klein--Gordon oscillator eigenfunctions is proved in one and three spatial dimensions. The proofs establish the closure relations satisfied by the eigenfunctions and are based on standard properties of the Hermite and the generalized Laguerre polynomials, supplemented in three dimensions by the completeness of the spherical harmonics. The scalar nature of the Klein--Gordon field renders the argument strictly simpler than the analogous proof for the Dirac oscillator: no off-diagonal cancellation is required. Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2605.21791 [quant-ph] (or arXiv:2605.21791v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.21791 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kevin Giovanni Hernández Beltrán [view email] [v1] Wed, 20 May 2026 22:32:49 UTC (16 KB) Full-text links: Access Paper: View a PDF of the paper titled Completeness of the Klein-Gordon oscillator eigenfunctions via Hermite and Laguerre polynomials, by Kevin Hern\'andezView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)