Diatomic molecule: V(r) = Dₑ(1 − e^{−a(r−rₑ)})² with quantized vibrational levels
The Morse potential models real diatomic bond stretching (unlike the harmonic oscillator). It admits a finite number of bound states Eₙ = ℏω₀(n+½) − ℏ²ω₀²(n+½)²/4Dₑ, plus a continuum above Dₑ (dissociation). The anharmonicity causes unequal energy level spacing — exactly observed in IR spectra.