We give a proof of the duality relation 〈σbound〉〈σfree〉 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 Hulth\'en potentials.
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Durand et al. (1981) studied this question.
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