Some matrix elements for Morse oscillators

In this paper general working equations for the Morse ${(r-r_e)}^l$ matrix elements are given. These equations can be used to calculate the diagonal ($m=n$) matrix elements and, for the off-diagonal ($m\ne n$) elements, are simpler to use than the ones currently available in the literature. Also, in this paper a new approach is given which allows one to obtain simple formulas, in closed form, for the off-diagonal matrix elements. Explicit expressions are given for $l=1, 2, \mathrm{and} 3$.