Propagator for finite range potentials: The case of reflection

Following a previous study on the transmission propagator for a finite range potential, the problem of reflection is considered. It is found that the Laplace transform of the reflection propagator can be expressed in terms of the usual Fredholm determinant Δ and of a new similar determinant Γ, containing the peculiar characteristics of reflection. As an example, an array of delta potentials is considered. Moreover, a possible application to the calculation of quantum traversal time is shown