## Physics & Astronomy

#### Event Title

An Exactly Solvable Model for Quantum Resonances: The Friedrichs Model

#### Document Type

Oral Presentation

#### Location

Indianapolis, IN

#### Start Date

13-4-2018 9:00 AM

#### End Date

13-4-2018 10:15 AM

#### Sponsor

Gonzalo Ordonez (Butler University)

#### Description

The Friedrichs model consists in an interaction between the bound state of a quantum system (say, an atom) and an external field, interaction which produces a resonance. This interaction intertwines the bound state with the eigenvectors of the continuous spectrum of the field Hamiltonian and depends on a coupling parameter. The resonance appears as a pole of the analytic continuation of the reduced resolvent corresponding to the interacting Hamiltonian. This model admits generalizations like, for instance, adding bound states and/or degeneracy to the field Hamiltonian. We examine what happens as the imaginary component of the eigenvalue associated with a resonant energy approaches zero.

An Exactly Solvable Model for Quantum Resonances: The Friedrichs Model

Indianapolis, IN

The Friedrichs model consists in an interaction between the bound state of a quantum system (say, an atom) and an external field, interaction which produces a resonance. This interaction intertwines the bound state with the eigenvectors of the continuous spectrum of the field Hamiltonian and depends on a coupling parameter. The resonance appears as a pole of the analytic continuation of the reduced resolvent corresponding to the interacting Hamiltonian. This model admits generalizations like, for instance, adding bound states and/or degeneracy to the field Hamiltonian. We examine what happens as the imaginary component of the eigenvalue associated with a resonant energy approaches zero.