The Kepler Problem in Two-Dimensional Momentum Space

Abstract

Fock studied the hydrogen atom problem in momentum space by projecting the space into a 4-dimensional hyperspherical space. He found that as a consequence of the symmetry of the problem in this space the eigenfunctions are the R4 spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this paper we note that if his method is applied to the 2-dimensional Kepler problem in momentum space, the eigenfunctions are R3 spherical harmonics, Ylm, and the eigenvalues are determined only by the quantum number l. These facts enable one to give a visualizable geometrical discussion of the dynamical degeneracy.