Arbitrary l-state solutions of the rotating Morse potential through the exact quantization rule method

By using the exact quantization rule, for non-zero l   values we present analytical solutions of the radial Schrödinger equation for the rotating Morse potential in the frame of the Pekeris approximation. The energy levels of all the bound states are easily calculated from this quantization rule. Especially, the intractable normalized wavefunctions are also obtained. The numerical calculations for three typical diatomic molecules HCl, CO and LiH are compared with those obtained by other methods such as the supersymmetry, the Fourier gird Hamiltonian, the asymptotic iteration, the variational, the Nikiforov–Uvarov, the shifted 1/N1/N expansion and the modified shifted 1/N1/N expansion. It is found that the results obtained by the present method are in good agreement with those obtained by other approximate methods.