Stationary scattering can be described by imposing finite box boundary conditions to the wave function. This implies a discretization of the scattering quantities and allows their determination by means of standard square integrable techniques. In particular, there exists a connection between the spectral properties of the Hamiltonian in the finite box and the scattering phase shift. In this paper the finite box discretization is reviewed, a way to overcome some of the drawbacks of the usual discrete-continuum connection for the phase shift is indicated, and a new procedure is examined to discretize the transition matrix with the aid of an analytically solvable potential model.