Analytic Properties of the Jost Functions via the Poincar\'e-Picard Theorem
Summarize this article with:
Quantum Physics arXiv:2605.28859 (quant-ph) [Submitted on 21 May 2026] Title:Analytic Properties of the Jost Functions via the Poincaré-Picard Theorem Authors:Yannick Mvondo-She View a PDF of the paper titled Analytic Properties of the Jost Functions via the Poincar\'e-Picard Theorem, by Yannick Mvondo-She View PDF HTML (experimental) Abstract:The analytic properties of the Jost functions are fundamental in quantum scattering theory and in the analytic continuation of the scattering matrix into the complex energy plane. In this work, the analyticity of the Jost functions is investigated from the perspective of parameter-dependent ordinary differential equations. Starting from the radial Schrödinger equation for a short-range central potential, a first-order differential system is derived for the coefficient functions associated with the Ricatti--Bessel and Ricatti--Neumann solutions. The multivalued dependence on the energy variable is shown to originate from the square-root relation between energy and momentum. By explicitly factorizing the momentum-dependent branching terms, the scattering problem is transformed into a differential system whose coefficients are single-valued analytic functions of the complex energy. Using the classical theory of analytic dependence of solutions of ordinary differential equations on parameters, it is shown that the transformed Jost functions are single-valued analytic functions of the energy variable for finite radial distance. The geometric interpretation of the factorization procedure is also discussed in terms of the topology of the associated Riemann surface. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2605.28859 [quant-ph] (or arXiv:2605.28859v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.28859 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yannick Mvondo-She [view email] [v1] Thu, 21 May 2026 16:52:27 UTC (24 KB) Full-text links: Access Paper: View a PDF of the paper titled Analytic Properties of the Jost Functions via the Poincar\'e-Picard Theorem, by Yannick Mvondo-SheView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: hep-th 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?)