  A number of approaches to the arrival time problem employ a complex potential
of a simple step function type and the arrival time distribution may then be
calculated using the stationary scattering wave functions. Here, it is shown
that in the Zeno limit (in which the potential becomes very large), the arrival
time distribution may be obtained in a clear and simple way using a path
integral representation of the propagator together with the path decomposition
expansion (in which the propagator is factored across a surface of constant
time). This method also shows that the same result is obtained for a wide class
of complex potentials.
