Abstract
The semigroup decomposition formalism makes use of the functional model for C0 class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.
Original language | English |
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Article number | 123505 |
Journal | Journal of Mathematical Physics |
Volume | 47 |
Issue number | 12 |
DOIs | |
State | Published - 2006 |
Bibliographical note
Funding Information:The work of Y.S. was partially supported by ISF under Grants No. 1282/05 and No. 188/02, and by the Center for Advanced Studies in Mathematics at Ben-Gurion University and the Edmond Landau Center for research in Mathematical Analysis and related areas, sponsored by the Minerva Foundation (Germany).
Funding
The work of Y.S. was partially supported by ISF under Grants No. 1282/05 and No. 188/02, and by the Center for Advanced Studies in Mathematics at Ben-Gurion University and the Edmond Landau Center for research in Mathematical Analysis and related areas, sponsored by the Minerva Foundation (Germany).
Funders | Funder number |
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Center for Advanced Studies in Mathematics | |
Minerva Foundation | |
Israel Science Foundation | 1282/05, 188/02 |
Ben-Gurion University of the Negev |