Geometric quantization of the multidimensional Kepler problem

Abstract

The geometric quantization scheme of Czyz and Hess is applied to the (n - 1)-dimensional quadric in complex projective space. As the quadratic is the orbit manifold of the n-dimensional Kepler problem and the geodesic flow on the n-dimensional euclidean sphere, we thus obtain the quantum energy levels and their multiplicities for these Hamiltonian systems.