2006/07/24 by Rafael de la Madrid, R. de la Madrid · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.2563170
published as AIPConf.Proc.885:3-25,2007 · 23 pages; written version of the five-lecture course delivered at the 2006 Summer School of CINVESTAV, Mexico City, July 2006
arxiv created 2006/07/24 · openalex publication_date 2007/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
The spectrum of a quantum system has in general bound, scattering and resonant parts. The Hilbert space includes only the bound and scattering spectra, and discards the resonances. One must therefore enlarge the Hilbert space to a rigged Hilbert space, within which the physical bound, scattering and resonance spectra are included on the same footing. In this work, I will explain how this is done.