The Energy Levels of a Rotating Vibrator

TLDR: In this paper, the energy levels of a rotating vibrator are calculated in considerable detail by means of the Wentzel-Brillouin-Kramers method and a set of correction terms which appear in the earlier members of the equation are determined.

Abstract: The energy levels of a rotating vibrator are calculated in considerable detail by means of the Wentzel-Brillouin-Kramers method. The new terms determined are ${\ensuremath{\omega}}_{e}z$ and a set of correction terms which appear in the earlier members of the equation. These correction terms enter in such a way that ${\ensuremath{\omega}}_{e}$ is not exactly the coefficient of ($v+\frac{1}{2}$); ${B}_{e}$ is not exactly the coefficient of $K(K+1)$, etc. However the differences are small and are detectable only in the case of light molecules. The correction terms are of the magnitude of $\frac{{{B}_{e}}^{2}}{{{\ensuremath{\omega}}_{e}}^{2}}$. Formulas for the effect of the correction terms on isotope shifts are given, and for the calculation of the correction terms themselves. Also a method is given for obtaining actual potential functions from band spectrum data, based on Morse's potential function. Finally the numerical magnitude of the correction terms for several states of ${\mathrm{H}}_{2}$ and for NaH is discussed.