An Asymptotic Expression for the Energy Levels of the Rigid Asymmetric Rotor

Abstract

The energy matrix of the rigid asymmetric rotor, evaluated in terms of symmetric rotor wave functions, has been examined under conditions where J is increased indefinitely. Asymptotically, the energy matrix assumes a form that is very much like the matrix that may be obtained from the characteristic value problem of Mathieu's differential equation. The characteristic values of Mathieu's equation serve as the basis for a good approximation to the energy values of those asymmetric rotor levels which, for a given, large value of J, correspond to a small value of K in the limiting symmetric cases. The differences which exist between the two matrices are accounted for by a perturbation technique which permits an accurate determination of the energy values. When the characteristic values of Mathieu's equation lead to a successful approximation to the energy values of the asymmetric rotor, an estimate may be made of the asymmetric rotor wave functions.