Duality for heavy-quark systems

We give a proof of the duality relation $〈{\sigma }_{\mathrm{bound}}〉\simeq 〈{\sigma }_{\mathrm{free}}〉$ for nonrelativistic potential models, using Feynman propagators. There are important and calculable corrections to the duality relation, both for smooth long-range potentials and for singular short-range potentials. We illustrate the corrections for the exactly solvable harmonicoscillator, linear, and Hulthén potentials.