A Note on the Theory of Vibration-Rotation Interaction

Attempts to treat the differential equation for the radial component of the Eigenfunktion of a rotating harmonic oscillator by the W.K.B. or alternative methods, have encountered difficulties because of the nature of the equation. The interval from $r=0\mathrm{}$ to $r=\infty$, on which the equation has to be considered, includes both a singular point and a turning point. About these points the Stokes' phenomenon is involved, and the elementary asymptotic solutions fail to remain valid. Known theory which is applicable to the equation in intervals which contain such critical points is here called upon to yield an equation for the Eigenwerte, and to produce descriptions of the solutions over the complete range of the variable.