Approximate resonance states in the semigroup decomposition of resonance evolution

Journal of Mathematical Physics (Impact Factor: 1.18). 01/2007; DOI: 10.1063/1.2383069
Source: arXiv

ABSTRACT The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ 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.

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