401-1001-57L  Kepler Problem

SemesterSpring Semester 2018
LecturersH. Knörrer
Periodicitynon-recurring course
Language of instructionGerman

AbstractThe 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.
ObjectiveUnderstanding of techniques for the solution and symmetries of classical physical problems.
ContentVarious 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
LiteratureV.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