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The behavior of both the survival S(t) and nonescape P(t) probabilities atlong times for the one-dimensional free particle system is shown to be closelyconnected to that of the initial wave packet at small momentum. We prove thatboth S(t) and P(t) asymptotically exhibit the same power-law decrease at longtimes, when the initial wave packet in momentum representation behaves as O(1)or O(k) at small momentum. On the other hand, if the integer m becomes greaterthan 1, S(t) and P(t) decrease in different power-laws at long times.Comment: 4 pages, 3 figures, Title and organization changed, however the  results not changed, To appear in Phys. Rev.

Free initial wave packets and the long-time behavior of the survival and nonescape probabilities