Quantum bootstrap for central potentials
Summarize this article with:
Quantum Physics arXiv:2512.09041 (quant-ph) [Submitted on 9 Dec 2025] Title:Quantum bootstrap for central potentials Authors:Scott Lawrence, Brian McPeak View a PDF of the paper titled Quantum bootstrap for central potentials, by Scott Lawrence and Brian McPeak View PDF HTML (experimental) Abstract:We study the quantum-mechanical bootstrap as it applies to the bound states of several central potentials in three dimensions. As part of this effort, we show how the bootstrap approach may be applied to ``non-algebraic'' potentials, such as the Yukawa potential (which asymptotically decays as an exponential) and a Gaussian potential. We additionally review the bootstrap of the Coulomb potential, demonstrate a high-precision bootstrap of the Cornell potential, and study conformal quantum mechanics. These results further recommend the bootstrap as a numerical method for high-precision calculations of ground-state physics, where applicable: for example, we are able to determine the critical coupling in the Cornell potential to better than one part in $10^7$, the most precise determination to date. Lower bounds on energies are also of high precision, occasionally one part in greater than $10^8$. Finally, we discuss the circumstances under which we are able to obtain meaningful upper bounds on ground-state energies. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Lattice (hep-lat); High Energy Physics - Theory (hep-th) Report number: LA-UR-25-31761 Cite as: arXiv:2512.09041 [quant-ph] (or arXiv:2512.09041v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.09041 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Scott Lawrence [view email] [v1] Tue, 9 Dec 2025 19:00:23 UTC (318 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum bootstrap for central potentials, by Scott Lawrence and Brian McPeakView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: hep-lat 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)