  A remarkable quantitative agreement is found between the non-Markovian
quantum kinetic approach and the time-dependent Dirac equation approach for a
large region of Keldysh parameter, in the investigation of electron-positron
pair production in the electric fields which is spatially homogeneous and
envelope pulse shaped. If a sub-critical bound potential is immersed in this
background field, the TDDE results show that the creation probability will be
enhanced by the bound states resonance by two orders of magnitude. We also
establish a computing resources greatly saved TDDE formalism for spatially
homogeneous field.

Quantum Physics;Computational Physics