  The bound state energy eigenvalues for the two-dimensional Kepler problem are
found to be degenerate. This "accidental" degeneracy is due to the existence of
a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector.
Reformulating the problem in momentum space leads to an integral form of the
Schroedinger equation. This equation is solved by projecting the
two-dimensional momentum space onto the surface of a three-dimensional sphere.
The eigenfunctions are then expanded in terms of spherical harmonics, and this
leads to an integral relation in terms of special functions which has not
previously been tabulated. The dynamical symmetry of the problem is also
considered, and it is shown that the two components of the Runge-Lenz vector in
real space correspond to the generators of infinitesimal rotations about the
respective coordinate axes in momentum space.
