On the variational solution of the coupled breathing rotation-vibration of a spherical top molecule

摘要

On the basis of the solutions of the isotropic 3-D harmonic oscillator, we show how to evaluate the matrix elements for the coupled rotation-vibration of the totally symmetric breathing mode of a rotating spherical top molecule, whereby the anharmonic potential energy is expanded in a power series of r. It is shown also how to obtain the ro-vibrational spectrum when used in conjunction with the variational method to obtain eigenvalues.