We present a systematic perturbative method for calculating the bindin
g energies of ro-vibrational quantum states for a finite depth potenti
al. Using an asymptotic expansion in powers of 1/eta, where eta is the
dimensionless physical depth parameter, explicit calculations are per
formed. Our analytic results lead to highly convergent series for the
binding energies, and numerical results for realistic potentials such
as Morse and Lennard-Jones potentials are found to be in excellent agr
eement with the exact ones.