Abstract

LEY-KOO, E  and  MENDEZ-FRAGOSO, R. Rotational states of asymmetric molecules revisited: matrix evaluation and generating function of Lamé functions. Rev. mex. fis. [online]. 2008, vol.54, n.2, pp.162-172. ISSN 0035-001X.

The solutions of the Schrödinger equation describing rotational states of asymmetric molecules are known to be separable as products of Lame 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 Lame 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.

Keywords : Asymmetric molecules; rotation spectra; matrix evaluation; spherical harmonics; Lame functions; spheroconal harmonics; generating function.

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