401-1001-57L Kepler Problem
| Semester | Spring Semester 2018 |
| Lecturers | H. Knörrer |
| Periodicity | non-recurring course |
| Language of instruction | German |
| Abstract | The Keplerproblem is the problem of the motion of a point mass in the gravitational field of another point mass. We shall discuss various approaches to this problem, in classical, in quantum mechanics and in relativity. |
| Objective | Understanding of techniques for the solution and symmetries of classical physical problems. |
| 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. The Schwarzschild metric |
| 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. Birkhäuser 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 L.Landau, E.Lifschitz: Quantenmechanik N.Woodhause: General Relativity. Springer Verlag 2007 |