The quantum mechanical three-body problem and its application to nonlinear, triatomic molecules

Abstract

The main problem in the theory of the rotational and vibrational levels in triatomic molecules is the introduction of a suitable coordinate system. After separation of the center-of-mass motion, a set of normal coordinates describing the oscillations and three Eulerian angles defining the orientation of a “body-fixed” coordinate system in space are introduced. Since the molecule has no rigid configuration, the body-fixed system can be defined in different ways. In the present paper, the latter has been chosen to be the instantaneous system of principal axes of inertia. This leads, however, to serious difficulties in the interpretation of the moments of inertia as mentioned by Eckart in 1934. In this paper it is shown how these difficulties may be overcome by means of a unitary transformation. The results of our theory are found to be in agreement with those of the former theory with some differences concerning definition of the empirical parameters.