Multi-channel Green's functions in complete L² bases

The matrix representation of the reference Hamiltonian, H₀, which may be either the free kinetic energy operator or the Coulomb Hamiltonian, is tridiagonal in the complete Laguerre or oscillator bases of L²(0, ∞). In either of these two bases, we explicitly find a closed-form solution to the matrix elements of the multichannel Green's function associated with the model Hamiltonian H = H₀ + Ṽ. Here the model potential, Ṽ^αβ, is constructed from the given short range multichannel potential, V^αβ, by restricting it to the subspace spanned by the first N_α member of the αth channel basis and the first N_β member of the βth channel basis. Subsequently, we solve the multichannel Lippman-Schwinger equation and find explicit forms for both the T- and S-matrices.