  The trigonometric P\"oschl-Teller (PT) potential describes the diatomic
molecular vibration. We have obtained the approximate solutions of the radial
Schr\"odinger equation (SE) for the rotating trigonometric PT potential using
the Nikiforov-Uvarov (NU) method. The energy eigenvalues and their
corresponding eigenfunctions are calculated for arbitrary -states in closed
form. In the low screening region, when the screening parameter the potential
reduces to Kratzer potential. Further, some numerical results are presented for
several diatomic molecules.
