  Bound states of the Hellmann potential, which is a superposition of the
attractive Coulomb ($-A/r$) and the Yukawa ($Be^{-Cr}/r$) potential, are
calculated by using a generalized pseudospectral method. Energy eigenvalues
accurate up to thirteen to fourteen significant figures, and densities are
obtained through a nonuniform, optimal spatial discretization of the radial
Schr\"odinger equation. Both ground and excited states are reported for
arbitrary values of the potential parameters covering a wide range of
interaction. Calculations have been made for higher states as well as for
stronger couplings. Some new states are reported here for the first time, which
could be useful for future works. The present results are significantly
improved in accuracy over all other existing literature values and offers a
simple, accurate and efficient scheme for these and other singular potentials
in quantum mechanics.
