caa a22 4500 463197194 CHVBK 20180406164926.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s10773-006-9324-8 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9324-8 Courbage Maurice Laboratoire de Physique Théorique de la Matière Condensée, Université Paris 7 - Denis Diderot, Fédération Matière et Systèmes Complexes, Tour 24-14.5ème étage, 4, Place Jussieu, 75251, Paris Cedex 05, France aut Semi-Groups and Time Operators for Quantum Unstable Systems [Elektronische Daten] [Maurice Courbage] We use spectral projections of time operator in the Liouville space for simple quantum scattering systems in order to define a space of unstable particle states evolving under a contractive semi-group. This space includes purely exponentially decaying states that correspond to complex eigenvalues of this semi-group. The construction provides a probabilistic interpretation of the resonant states characterized in terms of the Hardy class. Springer Science+Business Media, LLC, 2007 quantum ustable system nationallicence time operator nationallicence semigroup time evolution nationallicence Hardy spaces nationallicence Liouville spaces nationallicence International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/8(2007-08-01), 1881-1889 0020-7748 46:8<1881 2007 46 10773 https://doi.org/10.1007/s10773-006-9324-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9324-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Courbage Maurice Laboratoire de Physique Théorique de la Matière Condensée, Université Paris 7 - Denis Diderot, Fédération Matière et Systèmes Complexes, Tour 24-14.5ème étage, 4, Place Jussieu, 75251, Paris Cedex 05, France aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/8(2007-08-01), 1881-1889 0020-7748 46:8<1881 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer