Geometric View of One-Dimensional Quantum Mechanics
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Quantum Physics arXiv:2512.23923 (quant-ph) [Submitted on 30 Dec 2025] Title:Geometric View of One-Dimensional Quantum Mechanics Authors:Eren Volkan Küçük View a PDF of the paper titled Geometric View of One-Dimensional Quantum Mechanics, by Eren Volkan K\"u\c{c}\"uk View PDF HTML (experimental) Abstract:We apply De Haro's Geometric View of Theories to one of the simplest quantum systems: a spinless particle on a line and on a circle. The classical phase space M = T*Q is taken as the base of a trivial Hilbert bundle E ~ M x H, and the familiar position and momentum representations are realised as different global trivialisations of this bundle. The Fourier transform appears as a fibrewise unitary transition function, so that the standard position-momentum duality is made precise as a change of coordinates on a single geometric object. For the circle, we also discuss twisted boundary conditions and show how a twist parameter can be incorporated either as a fixed boundary condition or as a base coordinate, in which case it gives rise to a flat U(H)-connection with nontrivial holonomy. These examples provide a concrete illustration of how the Geometric View organises quantum-mechanical representations and dualities in geometric terms. Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph) Cite as: arXiv:2512.23923 [quant-ph] (or arXiv:2512.23923v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.23923 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Eren Volkan Küçük [view email] [v1] Tue, 30 Dec 2025 00:48:29 UTC (13 KB) Full-text links: Access Paper: View a PDF of the paper titled Geometric View of One-Dimensional Quantum Mechanics, by Eren Volkan K\"u\c{c}\"ukView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: physics physics.hist-ph 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?)