Abstract
Fock (1935) explained the degeneracy of the energy levels of the Kepler problem (or hydrogen atom) in terms of the dynamical symmetry group SO(4). He showed that the problem is equivalent to the geodesic flow on the sphere S3. The 'hidden' symmetry SO(4) is made manifest. The classical n-dimensional Kepler problem can be better understood by enlarging the phase space of the geodesical motion on Sn and including time and energy as canonical variables: a following symplectomorphism transforms the motion on Sn in the Kepler problem. The authors prove that the Fock procedure is the implementation at 'quantum' level of the above-mentioned symplectomorphism.
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