Coulomb problem for a Dirac particle in flat Minkowski space and the Heun functions, extension to curved models

2011/09/26 by Е. М. Ovsiyuk, E. M. Ovsiyuk, Ovsiyuk, E. M. +3
Mathematics · Physics and Astronomy · #35 #Algebraic and Geometric Analysis #FOS: Physical sciences #G.1 #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #acm:35 #math-ph #math.MP #msc:35

paper · pdf · doi:10.48550/arxiv.1109.5452

22 pages

arxiv created 2011/09/26 · openalex publication_date 2011/09/26 · arxiv updated 2011/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that there exist several ways to treat the quantum-mechanical Coulomb problem for a Dirac particle in flat Minkowski space with the help of the Heun differential equation, Fuchs's equation with four singular points. When extending the problem to curved spaces of constant curvature, Lobachevsky H₃ and Rimann S₃, there arise 2-nd order differential equations of the Fuchs type with 6 singular points, a method to get relevant equations with five singular points has been elaborated.

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