Geodesic
Multichannel Green's functions and perturbation theory for multichannel problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 3, pp. 338-342

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An expression is obtained for the Green's function of an $n$-channel one-dimensional Sehrödinger equation in terms of $2n$ linearly independent solutions of this equation in the general case and in terms of n linearly independent and channel-independent solutions in the case of an Hermitian matrix of the potentials. If these solutions are known, the construction of the perturbation theory series reduces to quadratures. 
@article{TMF_1984_58_3_a2,
     author = {A. I. Ignat'ev and V. S. Polikanov},
     title = {Multichannel {Green's} functions and perturbation theory for multichannel problems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {338--342},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_58_3_a2/}
}
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A. I. Ignat'ev; V. S. Polikanov. Multichannel Green's functions and perturbation theory for multichannel problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 3, pp. 338-342. http://geodesic.mathdoc.fr/item/TMF_1984_58_3_a2/