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Generalization of the amplitude-phase S-matrix formula for coupled scattering states
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-0149-341X
2005 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, Vol. 38, no 46, 10007-10013 p.Article in journal (Refereed) Published
Abstract [en]

The amplitude-phase method is generalized to coupled Schrodinger scattering states with a common angular momentum quantum number. A pair of expontentail-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-phase matrix solutions that are proportional to Jost-like Schrodinger 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.

Place, publisher, year, edition, pages
2005. Vol. 38, no 46, 10007-10013 p.
Keyword [en]
regge-pole positions, wave mechanics, residues, factorization, invariants, momentum
URN: urn:nbn:se:kth:diva-15227ISI: 000233696200010ScopusID: 2-s2.0-27844468653OAI: diva2:333268
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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