We study the problem of a particle hopping on the Bethe lattice in the
presence of a Coulomb potential. We obtain an exact solution to the particle's
Green's function along with the full energy spectrum. In addition, we present a
mapping of a generalized radial potential problem defined on the Bethe lattice
to an infinite number of one dimensional problems that are easily accessible
numerically. The latter method is particularly useful when the problem admits
no analytical solution.Comment: 5 pages + reference
