Rigorous test of the Raleigh-Ritz method for Mexican hat type potentials

Quantum Physics arXiv:2510.22233 (quant-ph) [Submitted on 25 Oct 2025] Title:Rigorous test of the Raleigh-Ritz method for Mexican hat type potentials Authors:A. M. Rodriguez Zarate, T. Thiemann View a PDF of the paper titled Rigorous test of the Raleigh-Ritz method for Mexican hat type potentials, by A. M. Rodriguez Zarate and 1 other authors View PDF HTML (experimental) Abstract:Interesting quantum integrable models are rare and one often has to resort to approximation methods. One of these is the Raleigh Ritz method which under certain circumstances allows to approximately compute the lowest energy eigenstate (or ground state) of a given Hamiltonian whose pure point spectrum is bounded from below. The quality of such approximations can then be tested numerically or sometimes by abstract arguments. However, the numerical test is limited by computing power. In order to perform a rigorous test, one would need to have at one's disposal 1. a physically interesting model that is 2. solvable to sufficient extent in order that 3. the exact ground state is known in closed form. In this contribution we show that certain anharmonic potentials of the Mexican hat type belong to this class of models. The corresponding Schroedinger type Hamiltonian can be considered as a crude quantum mechanical toy model Hamiltonian for the Higgs field in the standard model of elementary particle physics. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2510.22233 [quant-ph] (or arXiv:2510.22233v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.22233 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Thomas Thiemann [view email] [v1] Sat, 25 Oct 2025 09:29:42 UTC (25 KB) Full-text links: Access Paper: View a PDF of the paper titled Rigorous test of the Raleigh-Ritz method for Mexican hat type potentials, by A. M. Rodriguez Zarate and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 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?) 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?)