The Stark problem as a concave toric domain

2021/06/17 by Urs Frauenfelder, Frauenfelder, Urs
Mathematics · Physics and Astronomy · #53D20 #70H06 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG) #math.SG #msc:53D20 #msc:70H06

paper · pdf · doi:10.48550/arxiv.2106.09288

12 pages

arxiv created 2021/06/17 · openalex publication_date 2021/06/17 · arxiv updated 2021/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Stark problem is a completely integrable system which describes the motion of an electron in a constant electric field and subject to the attraction of a proton. In this paper we show that in the planar case after Levi-Civita regularization the bounded component of the energy hypersurfaces of the Stark problem for energies below the critical value can be interpreted as boundaries of concave toric domains.

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