Efficient numerical solution of the time-dependent Schrödinger equation for deep tunneling

The numerical challenge associated with the time-dependent approach to the general problem of the decay of a metastable state by quantum tunneling is discussed and methods towards its application to concrete problems are presented. In particular, different artificial boundary conditions were implemented in order to reduce the reflections of the wave packet at the numerical boundaries. They are illustrated and optimized for the deep tunneling case of ground state proton decay.

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