2003/11/10 by Sungyun Kim, Kim, Sungyun, Gonzalo Ordonez +2
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Atomic Physics (physics.atom-ph) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Applications #physics.atom-ph
paper · pdf · doi:10.48550/arxiv.physics/0311048
13 pages, 7 figures
openalex publication_date 2003/11/10 · arxiv created 2005/07/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a new unstable state in the Friedrichs model of a two-level atom. This unstable state is a complex eigenstate of the time evolution operator exp(-iHt) with a restricted test function space, which is obtained from causality conditions. The unstable state shows exact exponential decay for t≥0. Its emitted field is confined inside the future light-cone. In this way the long-standing problem of exponential catastrophe is removed. This is an example of quantum mechanics outside Hilbert space, which consists of generalized eigenstates in a distribution space, and a dual (test function) space.