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dc.contributor.author Bohm, A.R.
dc.contributor.author Gadella, M.
dc.contributor.author Kielanowski, P.
dc.date.accessioned 2019-02-14T16:55:51Z
dc.date.available 2019-02-14T16:55:51Z
dc.date.issued 2011
dc.identifier.citation Time Asymmetric Quantum Mechanics / A.R. Bohm, M. Gadella, P. Kielanowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 81Q65
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/147386
dc.description.abstract The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t₀≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics. uk_UA
dc.description.sponsorship This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html. We wish to acknowledge partial financial support by the Spanish Ministry of Science and Innovation through Project MTM2009-10751, the Junta de Castilla y Le´on, through Project GR224 and the US NSF Award no OISE-0421936. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Time Asymmetric Quantum Mechanics uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA

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