Semi-analytic evaluation of morse oscillator energies and wavefunctions in excited rotational states

A simple technique for generating accurate semi-analytic solutions for the one-dimensional Morse oscillator is presented. This modified Morse technique retains the simplicity and form of the j = 0 Morse solution but still satisfactorily includes the rotational features of the cases where j ≠ 0. The modified Morse solutions are compored to rigid rotor and exact numerical calculations performed by the finite element method. The technique is shown to give an accurate representation of the true wavefunction, and this result should make the method particularly useful for the generation of vibration-rotation transition matrix elements.