Approximate resonance states in the semigroup decomposition of resonance evolution

Details Approximate resonance states in the semigroup decomposition of resonance evolution Approximate resonance states in the semigroup decomposition of resonance evolution

2006-12-04

arxiv.org/abs/quant-ph/0612027v1

Physics

Quantum Physics

LaTex 22 pages 3 figures

Scientific paper

10.1063/1.2383069

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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