Knowledge Bank

The spectroscopically relevant nonvanishing RME^{\prime} of $rn$ for two-fold and threefold isotropic harmonic oscillators, for 0 $\le$ n $\le$ 7, and the diagonal element of $r8$, 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.