Morse Potential

Anharmonic molecular bond — V(r) = D(1 - e^(-a(r-r₀)))² — with quantized vibrational levels

Well depth D15.0

Width a0.80

r₀ (equilibrium)2.0

Animation40

Show harmonic1

Morse potential admits N_max = floor(D/ℏω - ½) bound states. Energy levels: Eₙ = ℏω(n+½) - (ℏω)²(n+½)²/(4D). Anharmonicity causes unequal level spacing and dissociation.