Transformation of perturbative series into complex phases and   elimination of secular divergences in time-dependent perturbation theory in   quantum mechanics
  The difficulty that the probabilities infinitely increase with time as time is long enough in time-dependent perturbation theory for some quantum systems is resolved by means of simply transforming the perturbative series into natural exponential functions of the re-summed perturbative series. Three exactly solvable models are taken to check our new formulation, and excellent agreements with the exact solution are achieved. 
Q. H. Liu
quant-ph