The Friedrichs Model and its use in resonance phenomena

Abstract

We present here a relation of different types of Friedrichs models and their use in the description and comprehension of resonance phenomena. We first discuss the basic Friedrichs model and obtain its resonance in the case that this is simple or doubly degenerated. Next, we discuss the model with $N$ levels and show how the probability amplitude has an oscillatory behavior. Two generalizations of the Friedrichs model are suitable to introduce resonance behavior in quantum field theory. We also discuss a discrete version of the Friedrichs model and also a resonant interaction between two systems both with continuous spectrum. In an Appendix, we review the mathematics of rigged Hilbert spaces.

105 pages

References in corpus (4)

• Bound states in the continuum in a single-level Fano-Anderson model
• Complex Energy Spectrum and Time Evolution of QBIC States in a Two-Channel Quantum wire with an Adatom Impurity
• The Friedrichs-Model with fermion-boson couplings
• The Friedrichs-Model with fermion-boson couplings II

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