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