A remark on the rate of regeneration in decay processes

It is shown that in decay process the regeneration of the undecayed unstable states from the decay products can not proceed too slowly (in a sense specified) at small time and correspondingly the deviation from exponential decay at small time can not be too small either. This is seen to be essentially a consequence of the semiboundedness of the Hamiltonian. As by product some sufficient conditions are obtained for the existence of certain operator limits that arise in the analysis of continuous observations in quantum mechanics and in the theory of generalized product formulas for semi-groups. (Auth.)