Schr\"{o}dinger equation is $\mathcal{R}$-separable in toroidal coordinates

Quantum Physics arXiv:2511.08646 (quant-ph) [Submitted on 10 Nov 2025] Title:Schrödinger equation is $\mathcal{R}$-separable in toroidal coordinates Authors:Matheus E. Pereira, Alexandre G. M. Schmidt View a PDF of the paper titled Schr\"{o}dinger equation is $\mathcal{R}$-separable in toroidal coordinates, by Matheus E. Pereira and 1 other authors View PDF HTML (experimental) Abstract:We present, for the first time, exact solutions for the Schrödinger equation in Moon and Spencer's toroidal coordinates, and in the electromagnetic toroidal--poloidal coordinate systems. Curiously, both systems present a fractional angular momentum, because of the torus's hole. We achieve these novel solutions using the irregular $\mathcal{R}$-separation of variables, an unexplored approach in Physics, which results in a wavefunction with fractional angular momentum eigenvalues. Numerous solutions for the Schrödinger equation in a variety of external potentials are shown, including an external magnetic field. A plane-wave expansion and a Green function are also presented, setting the stage for future progress in this area. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2511.08646 [quant-ph] (or arXiv:2511.08646v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.08646 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Matheus Elias Pereira [view email] [v1] Mon, 10 Nov 2025 21:12:13 UTC (4,284 KB) Full-text links: Access Paper: View a PDF of the paper titled Schr\"{o}dinger equation is $\mathcal{R}$-separable in toroidal coordinates, by Matheus E. Pereira and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 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?)