Propagator for finite range potentials

The Schroedinger equation in integral form is applied to the one-dimensional scattering problem in the case of a general finite range, non singular potential. A simple expression for the Laplace transform of the transmission propagator is obtained in terms of the associated Fredholm determinant, by means of matrix methods; the particular form of the kernel and the peculiar aspects of the transmission problem play an important role. The application to an array of delta potentials is shown.