Year: 2005
Type: article
Abstract: The amplitude-phase method is generalized to coupled Schrödinger scattering states with a common angular momentum quantum number. A pair of exponential-type amplitude-phase solutions u (±) j ( r )exp[±iϕ j ( r )] for each channel is obtained, containing a common complex scalar phase function ϕ 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 Schrödinger 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.
Author: Karl-Erik Thylwe
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2085875271