Interpreting Bohm quantum potentials in Computing quantum waves exactly from classical action
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Quantum Physics arXiv:2605.20443 (quant-ph) [Submitted on 19 May 2026] Title:Interpreting Bohm quantum potentials in Computing quantum waves exactly from classical action Authors:Winfried Lohmiller, Jean-Jacques Slotine View a PDF of the paper titled Interpreting Bohm quantum potentials in Computing quantum waves exactly from classical action, by Winfried Lohmiller and Jean-Jacques Slotine View PDF HTML (experimental) Abstract:The recent arXiv posting [11], commenting on the paper [7], argues that the proof of Lemma 3.1 in [7] is missing the Bohm quantum potential [1, 2] of the Madelung p.d.e. [9]. This short technical note extends the proof of Lemma 3.1 to introduce a Bohm quantum potential explicitly, and then shows why this term can be assumed to be zero in the wave construction, without loss of generality. The continuity p.d.e. and the Hamilton-Jacobi p.d.e., extended by the Bohm potential, are undisputed. However, the actual action and density solutions depend on their initialization at t = 0. In [7], this initialization is motivated by the Feynman kernel [4], which is fundamentally different from the standard initialization of the Madelung solution [9]. This in turn leads to different action and density solutions, and explains why in one case the Bohm quantum potential disappears and in the other does not. The resulting overall wave, however, is independent of this computational initialization. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.20443 [quant-ph] (or arXiv:2605.20443v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.20443 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Journal reference: Proceedings of the Royal Society A, 482(2336):20250413, 2026 Related DOI: https://doi.org/10.1098/rspa.2025.0413 Focus to learn more DOI(s) linking to related resources Submission history From: Winfried Lohmiller Wl [view email] [v1] Tue, 19 May 2026 19:55:40 UTC (30 KB) Full-text links: Access Paper: View a PDF of the paper titled Interpreting Bohm quantum potentials in Computing quantum waves exactly from classical action, by Winfried Lohmiller and Jean-Jacques SlotineView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)