Jost function for two-channel scattering problem

The Jost function is generalized to the case of two-channel scattering of nonrelativistic spinless particles with an arbitrary (not necessarily local) interaction Hamiltonian. It is shown that the problem of finding the Jost matrix from the $S$-matrix reduces to the solution of a nonsingular integral equation for a single function. An explicit solution for the Jost matrix can be found if the $S$-matrix can be continued analytically.