Generalization of the amplitude-phase S-matrix formula for coupled scattering states

摘要: The amplitude-phase method is generalized to coupled Schr?dinger scattering states with a common angular momentum quantum number. A pair of exponential-type solutions u(?)j(r)exp[?ij(r)] for each channel obtained, containing complex scalar phase function j(r) and two (column) vector amplitudes u(?)j(r). amplitude functions satisfy certain nonlinear Milne equations the product determines derivative function. Fundamental matrix that are proportional Jost-like constructed. It shown how S-matrix formula can be derived from Wronskian relations involving regular solution.