Ermakov-Lewis Invariants in Stationary Bohm-Madelung Quantum Mechanics
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Quantum Physics arXiv:2602.00507 (quant-ph) [Submitted on 31 Jan 2026] Title:Ermakov-Lewis Invariants in Stationary Bohm-Madelung Quantum Mechanics Authors:Anand Aruna Kumar View a PDF of the paper titled Ermakov-Lewis Invariants in Stationary Bohm-Madelung Quantum Mechanics, by Anand Aruna Kumar View PDF HTML (experimental) Abstract:The Ermakov Pinney equation and its associated invariant are shown to arise naturally in stationary quantum mechanics when the Schrodinger equation is expressed in Bohm Madelung form and the Hamiltonian is diagonal and separable. Under these conditions, the stationary continuity constraint induces a nonlinear amplitude equation of Ermakov Pinney type in each degree of freedom, revealing a hidden invariant structure that is independent of whether the evolution parameter is time or space. By reformulating the separated stationary equations in Sturm Liouville form and applying Liouville normalization, we demonstrate that the quantum potential is encoded as a curvature contribution of the self adjoint operator rather than appearing as an additional dynamical term. This correspondence preserves the standard probabilistic predictions of quantum mechanics while yielding exact stationary Bohmian amplitudes and their associated invariants. The resulting invariant-based formulation provides stationary guiding fields and clarifies the ontological status of Bohmian amplitudes as geometrically encoded structures rather than auxiliary dynamical additions. The results further show that stationary constrained Bohm Madelung systems naturally admit variational formulations whose extremals preserve the Ermakov Lewis invariant. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.00507 [quant-ph] (or arXiv:2602.00507v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.00507 Focus to learn more arXiv-issued DOI via DataCite Journal reference: International Journal of Quantum Foundations, Vol 12-2, 2026 Related DOI: https://doi.org/10.20944/preprints202601.0205.v1 Focus to learn more DOI(s) linking to related resources Submission history From: Anand Aruna Kumar [view email] [v1] Sat, 31 Jan 2026 04:34:43 UTC (64 KB) Full-text links: Access Paper: View a PDF of the paper titled Ermakov-Lewis Invariants in Stationary Bohm-Madelung Quantum Mechanics, by Anand Aruna KumarView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)