A new treatment of the vibration–Rotation eigenvalue problem for a diatomic molecule

Abstract

Abstract The problem of the determination of the vibration–rotation eigenvalue in diatomic molecules is considered. An eigenvalue equation totally independent from the eigenfunction is written for any potential, analytical or numerical. This equation uses uniquely the vibration–rotation canonical functions; its resolution is reduced to that of a simple and classical numerical problem. Examples of numerical applications for analytical (Morse) and numerical potentials are presented. It is shown that the vibrational eigenvalues deduced from the eigenvalue equation are within 10 –6 cm –1 of the exact values. Comparison with conventional methods are presented and discussed.