Rotational states of asymmetric molecules revisited: matrix evaluation and generating function of Lamé functions

Abstract

The solutions of the Schrödinger equation describing rotational states of asymmetric molecules are known to be separable as products of Lamé functions in spheroconal coordinates. However, the numerical evaluation of such solutions has not been implemented in efficient and practical ways. This paper overcomes this deficiency by presenting a matrix method for evaluating the needed Lamé functions, in their two kinds and eight species, to obtain accurate energy eigenvalues and eigenfunctions for the rotational states of molecules with any asymmetry. A generating function for these eigenfunctions, including its series expansions for any asymmetry, is also presented.