  We consider particles emanating from a source point inside an interval in
one-dimensional space and passing through detectors situated at the endpoints
of the interval that register their arrival time. Unambiguous measurements of
arrival or detection time are problematic in the orthodox narratives of quantum
mechanics, since time is not a self-adjoint operator. By contrast, the arrival
time at the boundary of a particle whose motion is being guided by a wave
function through the deBroglie-Bohm guiding law is well-defined and
unambiguous, and can be computationally feasible provided the presence of
detectors can be modeled in an effective way that does not depend on the
details of their makeup.
  We use an absorbing boundary condition for Dirac's equation (ABCD) proposed
by Tumulka, which is meant to simulate the interaction of a particle initially
inside a domain with the detectors situated on the boundary of the domain. By
finding an explicit solution, we prove that the initial-boundary value problem
for Dirac's equation satisfied by the wave function is globally well-posed, the
solution inherits the regularity of the initial data, and depends continuously
on it.
  We then consider the case of a pair of particles emanating from the source
inside the interval, and derive explicit formulas for the distribution of first
arrival times at each detector, which we hope can be used to study issues
related to non-locality in this setup.
