The Born-Oppenheimer approximation separates nuclear and electronic motion: electrons adjust instantly to nuclear positions, creating a potential energy surface V(R). For a diatomic molecule, a Morse potential V(R) = D_e(1−e^{−α(R−R_e)})² models the anharmonic well. Vibrational energy levels are quantized: E_n = ℏω(n+½) − anharmonic corrections.