  We tackle the problem of accurate simulations of switching currents arising
from tunnel events in the washboard potentials associated to Josephson
junctions. The measurements of the probability distribution of the switching
currents is essential to determine the quantum character of the device, and
therefore is at the core of technological applications, as Josephson junctions,
that have been proposed for quantum computers. In particular, we show how to
accurately calibrate the parameters of the boundary conditions to avoid
spurious reflections of the wavefunction from the finite border of numerical
simulations. The proposed approximate numerical scheme exploits a quantum
version of a prefect matched layers for the boundary problems associated with
this class of potentials. Thus, we employ the analogous of a well established
electromagnetic method to deal with radiation in mesoscopic quantum systems.
Numerical simulations demonstrate that the known analytic results are well
recovered in the appropriated limits of quantum measurements. We also find that
a relaxation time shows up in the dynamics of the quantum evolution in between
two consecutive measurements.
