General properties of the evolution of unstable states at long times

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.