FURTHER ANALYSIS OF SOLUTIONS TO THE TIME-INDEPENDENT WAVE-PACKET EQUATIONS OF QUANTUM DYNAMICS .2. SCATTERING AS A CONTINUOUS FUNCTION OF ENERGY USING FINITE, DISCRETE APPROXIMATE HAMILTONIANS

We consider further how scattering information (the S-matrix) can be o btained, as a continuous function of energy, by studying wave packet d ynamics on a finite grid of restricted size. Solutions are expanded us ing recursively generated basis functions for calculating Green's func tions and the spectral density operator. These basis functions allow o ne to construct a general solution to both the standard homogeneous Sc hrodinger's equation and the time-independent wave packet, inhomogeneo us Schrodinger equation, in the non-interacting region (away from the boundaries and the interaction region) from which the scattering solut ion obeying the desired boundary conditions can be constructed. In add ition, we derive new expressions for a ''remainder or error term,'' wh ich can hopefully be used to optimize the choice of grid points at whi ch the scattering information is evaluated. Problems with reflections at finite boundaries are dealt with using a Hamiltonian which is dampe d in the boundary region as was done by Mandelshtam and Taylor [J. Che m. Phys. 103, 2903 (1995)]. This enables smaller Hamiltonian matrices to be used. The analysis and numerical methods are illustrated by appl ication to collinear H+H-2 reactive scattering. (C) 1996 American Inst itute of Physics.