Limits of the harmonic approach for the Morse potential

Abstract

This paper presents the solution of the Morse potential via the Variational Method using a trial eigenfunction based on the harmonic oscillator and without variational parameters. The first fundamental state and the first nine excited states for the diatomic molecules of hydrogen, lithium hydride, sodium hydride, oxygen, carbon monoxide and silicon monoxide are calculated. The results obtained by the variational method are compared with the values obtained by the exact solution of the same potential in order to establish a percentage error for each energy level of the molecules analyzed and to verify up to which level the chosen trial eigenfunction describes the original system well. That shows that the approximation of the trial eigenfunction is reasonable for the first excited states. From the fourth or fifth excited state, depending on the molecule, the discrepancy no longer reasonable.