Abstract: The present paper developes a simple method for calculating the rovibrationally excited states of diatomic molecules. In principle, the results can retain the same accuracy as conventional numerical integration. As an example, the energy levels and wave functions of H_2 for the first 162 rovibrational states are given by this method.

Key words: Rovibrational states, Radial equation, Harmonic oscillator basis, Least squares fit