RADIAL MATRIX ELEMENTS OF $r^{n}$ FOR TWOFOLD AND THREEFOLD OSCILLATORS

Abstract

The spectroscopically relevant nonvanishing RME^{\prime} of $r^{n}$ for two-fold and threefold isotropic harmonic oscillators, for 0 $\leq$ n $\leq$ 7, and the diagonal element of $r^{8}$, have been formulated using the generating function for associated Laguerre $polynomials.^{1}$ An improved system of notation reveals symmetries and patterns which emerge as n increases, and streamlines computer programming of the RME^{\prime} s in molecular vibration problems.