Approximate resonance states in the semigroup decomposition of resonance evolution

Journal Article · Fri Dec 15 04:00:00 EST 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2383069· OSTI ID:20861564

Strauss, Y; Horwitz, L P; Volovick, A ^[1]

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1. Department of Mathematics, Ben-Gurion University of the Negev, Be'er Sheva 84105 (Israel)

The semigroup decomposition formalism makes use of the functional model for C{sub {center_dot}}{sub 0} 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.

• OSTI ID: 20861564
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DECOMPOSITION
ENERGY LEVELS
EVOLUTION
FUNCTIONAL MODELS
GROUP THEORY
HILBERT SPACE
MATRIX ELEMENTS
POTENTIALS
RESONANCE
SCATTERING