  The Schr\"odinger equation for diatomic molecules in deSitter and
anti-deSitter spaces is studied using the extended uncertainty principle
formulation. The equations are solved by the Nikiforov-Uvarov method for both
the Kratzer potential and the pseudoharmonic oscillator. The energy eigenvalues
of the system have been derived analytically, and the exact expressions of the
eigenfunctions are provided in terms of Romanovski and Jacobi polynomials. The
impact of the spatial deformation parameter on the bound states is also
examined, with experimental results used to establish an upper limit for this
parameter.
