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