Exact and Glauber amplitudes in multi-channel scattering

A model for one-dimensional many-channel scattering of a particle from a composite system is considered. It is assumed that the target cannot break up. Using Bellman's method of invariant embedding, a system of non-linear first-order differential equations with one-point boundary conditions is obtained for the transmission and reflection coefficients. These equations have stable numerical solutions. An alternative invariant embedding with the …