Factorization−method treatment of the perturbed Morse oscillator

By transforming the Morse oscillator from type B to type F factorization, we obtain operators for raising and lowering the vibrational quantum number v, and a recursion relation. This permits the calculation of matrix elements needed for perturbation of the Morse oscillator to any order for perturbations of the form (eau − 1)n. Explicit calculations are presented for n = 3 and n = 4, analogous to the usual cubic and quartic anharmonicity perturbations of the harmonic oscillator.