A New Analytical Approach to Study the ‎Anharmonic and Morse Potentials of ‎Diatomic Molecules

An appropriate analytical method has been used to solve the Schrödinger equation, for a polynomial anharmonic potential to obtain the eigen-energy levels, up to the second order. Moreover, the derived expression has been exploited in the case of the Morse potential that led to express the vibrational energy of diatomic molecules. The application of the proposed analytical method to some selected molecules makes it possible to obtain results that are in good agreement with those available in the literature, and proves that our approach can be a valuable aid in spectroscopic experiments.