Bound states of the hydrogen-like atomic systems in plasma environments

Quantum Physics arXiv:2607.19601 (quant-ph) [Submitted on 21 Jul 2026] Title:Bound states of the hydrogen-like atomic systems in plasma environments Authors:Fatma Zohra Khaled, Mustafa Moumni, Mokhtar Falek View a PDF of the paper titled Bound states of the hydrogen-like atomic systems in plasma environments, by Fatma Zohra Khaled and Mustafa Moumni and Mokhtar Falek View PDF HTML (experimental) Abstract:We conduct a non-relativistic study of plasma screening effects on hydrogen-like atomic systems using the Screened Coulomb Potential (SCP i.e. Yukawa potential). The radial Schrödinger equation is first reduced to a bi-confluent Heun (BCH) equation for the Killingbeck potential which is the truncated version of the SCP, and we write the exact BCH eigenfunctions and eigenenergies. We then study the limitations of these BCH solutions and obtain an analytic description valid for weak to moderate screening using the BCH functional form. The corrected eigenfunctions are constructed order by order up to O(k^3); they are expressed in terms of the Laguerre polynomials and reduces exactly to Coulomb eigenfunctions when k=0. Using these Functions, the energy spectrum is computed via two analytic methods: (i) direct evaluation of the full Yukawa Hamiltonian expectation value, and (ii) the Hellmann-Feynman theorem, yielding integral representation. All methods presented here provide explicit analytical formulas for both wavefunctions and eigenenergies valid for different ranges of the screening. These methods establish a powerful analytic framework for studying confined quantum systems. The thermodynamic properties are also derived using the BCH formulation. Comments: Subjects: Quantum Physics (quant-ph) MSC classes: 81Q15, 34B30, 82B30 ACM classes: J.2; G.1.2; G.1.7; F.2.1 Cite as: arXiv:2607.19601 [quant-ph] (or arXiv:2607.19601v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.19601 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mustafa Moumni [view email] [v1] Tue, 21 Jul 2026 22:04:20 UTC (1,053 KB) Full-text links: Access Paper: View a PDF of the paper titled Bound states of the hydrogen-like atomic systems in plasma environments, by Fatma Zohra Khaled and Mustafa Moumni and Mokhtar FalekView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)