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Communications in Mathematical Physics

A converse to a theorem by Friedrichs

Joseph Slawny

Published Sep 1, 1969• 1 citation
Publisher
DOI
10.1007/bf01645485

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1 The Friedrichs Model and its use in resonance phenomena.

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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.

•Jan 1, 2011•35 citations
Wolfgang Ernst Friedrich Pauli, a prominent scientist of modern physics, was born 120 years ago. Relates to his name among others the introduction of Pauli matrices and the proof of the theory of Spin Statistics Theorem. In 1925 created the most important theory, the Pauli exclusion principle, that two electrons cannot occupy the same quantum state. Recognition of his pioneer work won Nobel prize in 1945. Kivonat 120 éve született Wolfgang Ernst Friedrich Pauli, a modern fizika kiemelkedő személyisége. Nevéhez fűződik többek között a Pauli-mátrixok bevezetése és a spin-statisztika elméletének bizonyítása. 1925-ben alkotta meg legfontosabb elméletét, a Pauli-féle kizárási elvet, melynek legfontosabb tézise, hogy két elektron nem lehet ugyanabban a kvantumállapotban. E munkájáért 1945-ben fizikai Nobel-díjat kapott.
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.
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.