Reference potential approach to the energy eigenvalue problem of a rotating diatomic molecule

A two-stage analytical–numerical method is described, which enables to accurately solve the energy eigenvalue problem of a rotating oscillator. First, using a simple analytic algorithm, one constructs reliable Morse approximants to all rotational–vibrational states of the given effective potential. Thereafter, the Schrödinger equation is transformed into an equivalent pair of coupled first-order differential equations (Gordon equations), which are solved numerically. Integration step h = 0.05 Å is sufficient to ensure at least 6-digit accuracy for all energy levels of the examined model potential for H2 molecule.