

Article
Generalization of the amplitudephase Smatrix
formula for coupled scattering states
Authors: 
Thylwe, K.E. 
Document Type: 
Article 
Pubstate: 
Published 
Journal: 
J. Phys. A: Math. Gen. 
Volume: 
38
10071013 
Year: 
2005 
AbstractThe amplitudephase method is generalized to coupled Schr¨odinger scattering states with a common angular momentum quantum number. A pair of exponentialtype amplitudephase 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 amplitudephasematrix solutions that are proportional to Jostlike Schr¨odinger matrix solutions are constructed. It is shown how a generalized amplitudephase Smatrix formula can be derived from Wronskian relations involving the two amplitudephase matrix solutions and a regular matrix solution.

