Approximate resonance states in the semigroup decomposition of resonance evolution

Strauss, Y.; Horwitz, L. P.; Volovick, A.

Approximate resonance states in the semigroup decomposition of resonance evolution

Authors

Strauss, Y.

Horwitz, L. P.

Volovick, A.

Description

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.
LaTex 22 pages 3 figures