The European Physical Journal D

, Volume 54, Issue 1, pp 25–29 | Cite as

General properties of the evolution of unstable states at long times

  • K. UrbanowskiEmail author
Molecular Physics and Chemical Physics


An effect generated by the non-exponential behaviour of the survival amplitude of an unstable state at long times is considered. It is known that this amplitude tends to zero more slowly as t goes to infinity than any exponential function of t. Using methods of asymptotic analysis we find the asymptotic form of this amplitude at long times in a general, model-independent case. We find that the long time behaviour of this amplitude affects the form of the instantaneous energy of unstable states: this energy should be much smaller for suitably long times, t, than the energy of this state for t of the order of the lifetime of the considered unstable state.


03.65.-w Quantum mechanics 03.65.Ta Foundations of quantum mechanics; measurement theory 11.10.St Bound and unstable states; Bethe-Salpeter equations 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.University of Zielona Gora, Institute of PhysicsZielona GoraPoland

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