Energy levels for perturbed Morse oscillators

The energy levels and perturbation expansions for the expectation values of arbitrary powers of position for a perturbed Morse oscillator are obtained by application of the hypervirial and Hellmann–Feynman theorems, solely in terms of the unperturbed energy. We obtain expressions for the first-order corrections for (1 ? e^?aq )^m for 4 ? m ? 8 and the expressions to second and third order for the quartic perturbation. A numerical application to the CO molecule is made.