Current conservation and amplitude regularisation of the Landau problem: Bohm--Madelung description

Quantum Physics [Submitted on 14 Apr 2026] Current conservation and amplitude regularisation of the Landau problem: Bohm--Madelung description Anand Aruna Kumar This work investigates the dynamics of a charged particle in a uniform magnetic field within the Bohm--Madelung formulation of quantum mechanics. In this representation, the stationary Schrodinger equation separates into coupled amplitude and phase equations, where the amplitude sector admits a Sturm--Liouville structure supporting Ermakov--Lewis invariants. The analysis considers two complementary regularisation schemes: a global Fisher--information--based regularisation and a local canonical (shell) Bohm regularisation derived from stationary flux closure. These are applied within distinct classes of stationary flow, characterised by vanishing and nonvanishing component currents. It is shown that the radial and axial sectors remain globally regularisable, preserving analytic structure across the domain. In contrast, the azimuthal sector develops a nonseparable, generally complex-valued amplitude structure due to gauge-induced coupling. Nevertheless, a consistent local regularity is recovered at the level of canonical branches, where amplitude--momentum relations organise the solution in a well-defined manner. Regularisation thus acts as a structural reorganisation mechanism in amplitude space, preserving the Landau spectral scale while reorganising the flux-sector structure through branch-wise amplitude--momentum relations, thus establishing branch-wise organisation as a natural framework for describing stationary Bohmian dynamics in the Landau problem. Comments: 20 pages, V1, Map of analysis, appendix Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.12224 [quant-ph]   (or arXiv:2604.12224v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.12224 Focus to learn more Submission history From: Anand Aruna Kumar [view email] [v1] Tue, 14 Apr 2026 03:02:43 UTC (18 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)