Study for diatomic molecule by supersymmetric quantum mechanics approach and an identified method to Morse potential

For a diatomic molecule system in Morse potential the eigenfunctions and eigenvalues have been found by supersymmetric quantum mechanics (SQM) approach. The result has shown that Morse potential is shape invariance. A method identifying the Morse potential according to the energy spectrum of diatomic molecule has been suggested. Moreover, we also give the comprehension to shape invariance from space symmetry.