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

Authors: Thylwe, K.-E.
Document Type: Article
Pubstate: Published
Journal: J. Phys. A: Math. Gen.
Volume: 38   1007-1013
Year: 2005


The amplitude-phase method is generalized to coupled Schr¨odinger scattering states with a common angular momentum quantum number. A pair of exponential-type amplitude-phase solutions u^(±)_j (r) exp[±i\phi_j (r)] for each channel is obtained, containing a common complex scalar phase function \phi_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-phasematrix solutions that are proportional to Jost-like Schr¨odinger 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.