Using asymptotic iteration method (AIM) for solving differential equations: case study of vibrational states of diatomic molecule

Abstract

This paper discusses the new computational technique referred to as the asymptotic iteration method (AIM), and presents numerical computations of exact energy eigenvalues of the Schrödinger equation assuming the Morse potential for some diatomic molecules. The method is used to compute the numerical energies of bound vibrational levels of the 7Li₂, H₂, and N₂ diatomic molecules in the ?¹Σ_u+, 11Σ_u+ and ?³Σ_u+ electronic states.