A generalization of the Bargmann potentials to include the case of nonrelativistics-wave scattering of a particle by a target having a finite number of discrete excited states is presented. This generalization allows the explicit construction of a large class of many-channel S-matrices meromorphic on their energy Riemann surfaces as well as the explicit construction of the corresponding potential matrices. A two-channel example is treated in detail.
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Joseph R. Cox (1964) studied this question.
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