The connection between the rigged Hilbert space and the complex scaling approaches for resonances. The Friedrichs model

DOI10.1016/S0960-0779(01)00082-0zbMath1006.81022OpenAlexW2087272440WikidataQ127065787 ScholiaQ127065787MaRDI QIDQ1600478

Yu. B. Mel'nikov, E. A. Yarevskii, Ioannis E. Antoniou

Publication date: 13 June 2002

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(01)00082-0

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Exactly and quasi-solvable systems arising in quantum theory (81U15) Resonance in context of PDEs (35B34)

Related Items (4)

Krein-space formulation of \(\mathcal{PT}\) symmetry, \(\mathcal{CPT}\)-inner products, and pseudo-Hermiticity ⋮ PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS ⋮ The Friedrichs model and its use in resonance phenomena ⋮ Gamow vectors in a periodically perturbed quantum system

Cites Work

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• Extended spectral decompositions of the Rényi map
• Decaying states and the rigged Hilbert space formulation of quantum mechanics
• Dirac kets, Gamov vectors and Gel'fand triplets. The rigged Hilbert space and quantum mechanics. Lectures in mathematical physics at the University of Texas at Austin
• Resonances and the extension of dynamics to rigged Hilbert spaces

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