Multichannel Green's functions and perturbation theory for multichannel problems

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.