  We write Schr\"odinger equation for the Coulomb potential in both de Sitter
and Anti-de Sitter spaces using the Extended Uncertainty Principle formulation.
We use the Nikiforov-Uvarov method to solve the equations. The energy
eigenvalues for both systems are given in their exact forms and the
corresponding radial wave functions are expressed in associated Jacobi
polynomials for de Sitter space, while those of Anti-de Sitter space are given
in terms of Romanovski polynomials. We have also studied the effect of the
spatial deformation parameter on the bound states in the two cases.
