The rotational spectra of the most asymmetric molecules

Abstract

We consider the Schrödinger equation for the rotational spectra of the most asymmetric molecules. The energy eigenfunctions are also eigenfunctions of the square of the angular momentum vector and of one component of the angular momentum in the inertial frame. We follow our point of view in which the properties of the angular momentum spectra are used to delete, without loss of generality, one constant of motion and one of the Euler's angles. Then, instead of using Euler's angles, the Schrödinger equation and the energy eigenfunctions are expressed in terms of spheroconal coordinates in which that equation may be separable. The most asymmetric case is specially analyzed. The characteristic symmetries of this problem are used to reduce the number of differential equations considered and the number of steps for a complete solution.