In this work, we used the improved generalized Pöschl-Teller potential (IGPT) to calculate the rotational-vibrational (ro-vibrational, hereinafter) energies of potassium molecules in the excited electronic state (Formula presented.). In doing this, we first solved the Schrödinger equation for the (IGPT) by applying both the Pekeris-type and the Greene-Aldrich approximations to the centrifugal term. The obtained energy spectra are compared with that of the experimental Rydberg-Klein-Rees (RKR) data. We also showed that the IGPT potential is a good potential function in fitting experimental RKR data for the 39K2 ((Formula presented.)) molecule. Finally, we have proved that Pekeris-type approximation is better than Greene-Aldrich approximation in calculating the accurate ro-vibrational energies spectra for the (Formula presented.) potassium molecular dimers.
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