The Morse potential is a good approximation for a real potential to describe diatomic mo...

The Morse potential is a good approximation for a real potential to describe diatomic molecules. It is given by where D is the molecular dissociation energy, and r_e is the equilibrium distance between the atoms. For small vibrations, r - re is small, and V(r) can be expanded in a Taylor series to reduce to a simple harmonic potential. Find the lowest term of V(r) in this expansion and show that it is quadratic in (r - r_e).