Approximate resonance states in the semigroup decomposition of resonance evolution

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.

arXiv commentLaTex 22 pages 3 figures

References in corpus (5)

• A Pedestrian Introduction to Gamow Vectors
• Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space
• Generalized Eigenvectors for Resonances in the Friedrichs Model and Their Associated Gamov Vectors
• Stark Effect in Lax-Phillips Theory
• Lax-Phillips Scattering Theory of a Relativistic Quantum Field Theoretical Lee-Friedrichs Model and Lee-Oehme-Yang-Wu Phenomenology

Cited by in corpus (3)

• The rigged Hilbert space approach to the Gamow states
• Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution
• Transition Decomposition of Quantum Mechanical Evolution