Eur. Phys. J. D 54, 25-29 (2009)
https://doi.org/10.1140/epjd/e2009-00165-x

General properties of the evolution of unstable states at long times

University of Zielona Gora, Institute of Physics, ul. Prof. Z. Szafrana 4a, 65–, 516 Zielona Gora, Poland

Corresponding author: ^a K.Urbanowski@proton.if.uz.zgora.pl

Received: 29 December 2008
Revised: 18 February 2009
Published online: 6 June 2009

Abstract

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.