Quantization of the Linearized Kepler Problem

Details Quantization of the Linearized Kepler Problem Quantization of the Linearized Kepler Problem

2003-03-14

arxiv.org/abs/math-ph/0303037v1

Physics

Mathematical Physics

4 pages, Latex. To Appear in the Proceedings of GROUP24, Paris (France), July 2002

Scientific paper

The linearized Kepler problem is considered, as obtained from the Kustaanheimo-Stiefel (K-S)transformation, both for negative and positive energies. The symmetry group for the Kepler problem turns out to be SU(2,2). For negative energies, the Hamiltonian of Kepler problem can be realized as the sum of the energies of four harmonic oscillator with the same frequency, with a certain constrain. For positive energies, it can be realized as the sum of the energies of four repulsive oscillator with the same (imaginary) frequency, with the same constrain. The quantization for the two cases, negative and positive energies is considered, using group theoretical techniques and constrains. The case of zero energy is also discussed.

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