Abstract
In continuation of our previous paper of the anharmonic potentials analysis through the Floquet representation, we performed in this work a systematic calculation of the diatomic vibrational energy levels as well as the corresponding wave functions. The solution of Schrodinger equation according to Morse potential, which is a suitable model to describe the diatomic vibrational spectra, has been introduced; thus the explicit formulas to the second order have been established. As an illustration, the dissociation energies of some molecules species (i.e. ScN, LiH, Cl2 and NO) have been computed, as well as the wave functions and the corresponding probability densities, relating to the (ScN) molecule have been represented. Comparisons of our results with those of literature have been made.
Highlights
In view of the importance that has the harmonic, pseudo-harmonic and anharmonic oscillators in various fields of physics, they have been extensively used for solving most of physical problems
In continuation of our previous paper of the anharmonic potentials analysis through the Floquet representation, we performed in this work a systematic calculation of the diatomic vibrational energy levels as well as the corresponding wave functions
The solution of Schrödinger equation according to Morse potential, which is a suitable model to describe the diatomic vibrational spectra, has been introduced; the explicit formulas to the second order have been established
Summary
In view of the importance that has the harmonic, pseudo-harmonic and anharmonic oscillators in various fields of physics, they have been extensively used for solving most of physical problems. To this end, significant efforts are devoted to determining the general formulas of vibration-rotation energy spectra and wave functions for the molecular systems. It is impossible to find an exact solution to such systems, but one can apply conventional approximate methods usually presented in most standard textbooks and research papers [1] [2] [6] [7] In this regard, modeling the atomic potential is one of the most important parts of molecular dynamics. The Morse potential model provides an accurate description of the observed vibrational energy spectra of diatomic molecules, and has great popularity with chemists
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