Exact classical emergence from high-energy quantum superpositions

Quantum Physics arXiv:2605.16518 (quant-ph) [Submitted on 15 May 2026] Title:Exact classical emergence from high-energy quantum superpositions Authors:Juan A. Cañas, Daniel A. Bonilla, J. Bernal, A. Martín-Ruiz View a PDF of the paper titled Exact classical emergence from high-energy quantum superpositions, by Juan A. Ca\~nas and 3 other authors View PDF HTML (experimental) Abstract:We examine the correspondence principle for an equiprobable superposition of high-energy eigenstates of the infinite square well using a fully analytical Fourier-based approach. We derive a closed-form asymptotic expression for the interference terms $\rho_{\alpha}^{\text{a}}(x)$ by expanding them into a geometric series of quantum Fourier coefficients. We show these terms act as functional envelopes that do not vanish individually but become asymptotically equivalent in the large-$n$ limit. Furthermore, we prove the total probability density for a superposition of $2\Delta+1$ states converges exactly to the uniform classical distribution as $\Delta \to \infty$. Dynamically, the expectation value of position reproduces the classical triangular trajectory asymptotically. Residual quantum deviations remain confined to boundary layers whose relative width vanishes under macroscopic resolution. These results establish a rigorous asymptotic realization of the classical limit for isolated bound systems in both static and dynamical contexts. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2605.16518 [quant-ph] (or arXiv:2605.16518v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.16518 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Juan Antonio Cañas Palomeque [view email] [v1] Fri, 15 May 2026 18:12:03 UTC (1,390 KB) Full-text links: Access Paper: View a PDF of the paper titled Exact classical emergence from high-energy quantum superpositions, by Juan A. Ca\~nas and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math-ph math.MP 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?)