The Born-Oppenheimer approximation exploits the mass ratio m_e/M_N ≈ 1/2000: electrons equilibrate instantly as nuclei move. This yields a potential energy surface (PES) E_el(R) on which nuclear wavefunctions ψ_n(R) satisfy H_nuc = -ℏ²/(2M)∇² + E_el(R). For diatomics, the Morse potential V(R) = D_e(1-e^{-α(R-R_e)})² provides an accurate PES with exact vibrational eigenvalues E_v = ℏω_e(v+½) - ℏω_e x_e(v+½)². Non-adiabatic coupling occurs near conical intersections where two electronic surfaces touch — the BO approximation breaks down and geometric phase (Berry phase) appears.