Electron–positron pair creation is studied in the low-density approximation by solving the quantum Vlasov equation exactly and the mapping equation approximately. The simpler mapping equation is an approximate treatment of the quantum Vlasov equation in which the continuous external field is regarded as a series of delta kicks. Our study indicates that this new treatment is appropriate because the results of the two methods are in good agreement with each other. However, as the period number increases, interference and a complicated structure in the momentum distribution are observed. Furthermore, we also obtain the square power law relation of the number density to the applied electric field strength.