ABSTRACT
The numerical challenge associated with the time-dependent approach to the general problem of the decay of a metastable state by quantum tunnelling is discussed and methods towards its application to concrete problems are presented. In particular, a modification of the standard Crank-Nicolson method by a Numcrov-like formula leading to an improved accuracy in the approximation of second order spatial derivativo and different, artificial boundary conditions aimed to reduce the reflections of the wave packet at the numerical boundaries are described. One of these boundary conditions is adapted to the case of long range potentials, like Coulomb and centrifugal, which frequently appear in physical problems. The procedures are illustrated for the deep-tunnelling case of proton emission.
