Ground state energy of particle in space with minimal length and momentum
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Quantum Physics arXiv:2604.27018 (quant-ph) [Submitted on 29 Apr 2026] Title:Ground state energy of particle in space with minimal length and momentum Authors:Arsen Panas, Volodymyr Tkachuk View a PDF of the paper titled Ground state energy of particle in space with minimal length and momentum, by Arsen Panas and Volodymyr Tkachuk View PDF HTML (experimental) Abstract:In this article, we derive a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that is physically attainable. We consider a harmonic oscillator in such a space and calculate its ground state energy. We generalized the problem to an arbitrary potential, deriving an equation for the coordinate uncertainty corresponding to the minimal energy, which can be solved numerically. Using a linear approximation in the deformation parameters, we obtained a general expression for the ground-state energy. We determined the domain of existence of solutions for the anharmonic oscillator potential with respect to the deformation parameters. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.27018 [quant-ph] (or arXiv:2604.27018v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.27018 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Arsen Panas [view email] [v1] Wed, 29 Apr 2026 12:25:35 UTC (464 KB) Full-text links: Access Paper: View a PDF of the paper titled Ground state energy of particle in space with minimal length and momentum, by Arsen Panas and Volodymyr TkachukView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)