We consider further how scattering information (the S-matrix) can be obtained, as a continuous function of energy, by studying wave packet dynamics on a finite grid of restricted size. Solutions are expanded using recursively generated basis functions for calculating Green’s functions and the spectral density operator. These basis functions allow one to construct a general solution to both the standard homogeneous Schrodinger’s equation and the time-independent wave packet, inhomogeneous Schrodinger equation, in the non-interacting region (away from the boundaries and the interaction region) from which the scattering solution obeying the desired boundary conditions can be constructed. In addition, we derive new expressions for a "remainder or error term," which can hopefully be used to optimize the choice of grid points at which the scattering information is evaluated. Problems with reflections at finite boundaries are dealt with using a Hamiltonian which is damped in the boundary region as was done by Mandelshtam and Taylor [J. Chem. Phys. 103, 2903 (1995)]. This enables smaller Hamiltonian matrices to be used. The analysis and numerical methods are illustrated by application to collinear H+H-2 reactive scattering.