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Kepler Problem
Kepler-Problem
Last Updated: 2026-02-05 15:14:50
Abstract
The Keplerproblem is the problem of the motion of a point mass in the gravitational field of another point mass. We shal discuss various approaches to this problem, both in classical and in quantum mechanics.
Objective
Das Keplerproblem handelt von der Bewegung eines Massenpunktes im Gravitationsfeld eines anderen Massenpunktes. Wir wollen die verschiedenen Ansaetze, dieses Problem in der klassischen Mechanik und in der Quantenmechanik zu behandeln, studieren.
Content
Various derivations of the Kepler laws from Newton's laws. Anomalies and the Kepler equation. Hamiltonian formalism and integrable Hamiltonian systems. Symmetries and geometric regularizations of the Kepler problem. The hydrogen atom in quantum mechanics.
Resources
Literature
V.I.Arnold: Mathematical Methods of Classical Mechanics. Springer Verlag B.Cordani: The Kepler Problem. Birkh\"auser Verlag 2003 R.Cushman, L.Bates: Global Aspects of Classical Integrable Systems. Birkh\"auser Verlag 1997 D.Goodstein, J.Goodstein: Feynman's Lost Lecture. Random House 1996 J.Milnor: On the Geometry of the Kepler problem. American Mathematical Monthly {\bf 90}, 353-365 (1983) M.Valtonen, H.Karttunen: The Three Body Problem. Cambridge University Press 2006
General Information
- Language
- German
- Levels
- BSC
Examination
- Type
- end-of-semester examination
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Kepler-Problem |
|
2 h weekly |