  In the paper, a simple model of alpha decay with Dirac delta potential is
studied. The model leads to breakdown of the exponential decay and to power law
behavior at asymptotic times. Time dependence of the survival probability of
the particle in the potential well is analyzed numerically with two methods:
integration of Green's function representation and numerical solution of the
time-dependent Schr\"odinger equation. In particular, finite depth potential
wells and behavior between the exponential and power law regimes, which are
situations that could not be described in detail analytically, are studied. The
numerical results confirm power law with exponent n = 3 after the turnover into
the non-exponential decay regime. Moreover, the constructive and destructive
interference is observed in the intermediate stage of the process. The simple
alpha decay model is compared to the results of Rothe- Hintschich-Monkman
experiment which was the first experimental proof of violation of the
exponential law.
